Coba deh kamu pergi ke lapangan luas, lalu lihat ke sekitar. Seberapa jauh kamu bisa memandang? Ketika kamu melihat pohon di kejauhan, pasti akan kelihatan sangat keciiiiil. Eh, begitu kamu deketin pohonnya, ternyata ukurannya besar. Kok bisa gitu ya? Hal ini, disebabkan oleh perspektif.
Lalu, sekarang coba, deh, kamu tengok ke langit.
Apa yang kamu lihat?
Kalo yang kamu liat jemuran warga, geseran dikit dong.
Jemuran (sumber: merdeka.com)
Saat kita menatap langit, apalagi di malam hari, pasti hanya terlihat cahaya titik-titik putih. Sama halnya dengan perspektif tadi, titik putih yang sangat kecil ini, ternyata ukuran aslinya besaaar banget. Nah, titik-titik kecil di langit itu, sebenarnya bisa kita lihat dengan alat bantu. Namanya, teleskop atau teropong bintang.
Teropong bintang biasanya digunakan oleh para astronomer untuk mencari planet baru. Di alat ini, terdapat dua buah lensa cembung, yaitu lensa objektif yang berada di depan, yang menerima cahaya langsung dari objek. Dan lensa okuler, yaitu lensa yang berada dekat dengan pengamat.
Cara kerja teropong bintang adalah dengan metode “pengumpulan cahaya”. Sekarang bayangkan di rumah kamu sedang turun hujan. Lalu, kamu ambil ember dan tampung air hujannya. Pasti, deh, semakin besar ember yang kamu pakai, air yang kamu tampung juga semakin banyak. Nah, prinsip kerja teropong bintang kurang lebih kayak gitu. Tapi yang ditampung bukan air, melainkan cahaya.
Tampungan air hujan seperti cara mata dan teropong bintang bekerja (sumber:giphy.com)
Oke, kalau masih bingung. Kita mundur sedikit mengenai cara mata kita bekerja. Sejatinya, mata kita sama kayak “ember” yang menampung air hujan tadi. Bedanya, si air adalah “cahaya” yang ada di sekeliling kita dan ember yang menampung cahayanya adalah pupil mata kita. Cahaya-cahaya yang masuk ke dalam pupil, pada akhirnya ngebuat kita bisa melihat sekitar.
Pupil mata (sumber: gihpy.com)
Masalahnya, karena ukuran pupil mata kita kecil, cahaya yang masuk hanya sedikit.
Teropong bintang, membantu kita mengumpulkan cahaya-cahaya yang tidak jatuh ke mata kita, memfokuskannya, dan mengarahkannya langsung ke mata.
Anggap “ember penangkap cahaya” itu diberi lorong, dan di sana, cahaya-cahaya itu dikumpulkan, difokuskan, dan dikirim langsung menuju ke mata kita. Banyaknya jumlah cahaya yang dikumpulkan, tergantung dari area lensa teropong bintang yang kita lihat. Itu artinya, kalau kamu mengubah diameter teropong bintangnya menjadi dua kali lipat lebih besar, kita bakalan dapet cahaya sebanyak 4 kali lipat lebih banyak.
Bagaimana Teropong Bintang Bisa Mengumpulkan Cahaya?
Oke, sekarang bagaimana caranya si teropong bintang mengumpulkan cahaya supaya bisa masuk ke pupil mata kita? Bukan. Kamu jangan bayangin teropong bintang ini memungut cahaya kayak orang mungut recehan di jalan. Tetapi, membengkokkan cahaya yang ada di sekitar, dan mengarahkannya ke dalam teropong bintang.
Mengumpulkan uang receh (sumber: giphy.com)
Cara kerja teropong bintang itu mengubah arah cahaya dari suatu benda. Ya, cahaya selalu akan “berubah” arah apabila pindah dari satu medium ke medium lain. Itu lah kenapa kalau kamu memasukkan sendok ke dalam air, mata kita melihat seolah si sendok itu “patah” atau bengkok. Sendoknya gakpapa, tapi cahaya yang kita lihat bengkok, sehingga membentuk gambaran di kepala kita bahwa sendok yang ada di air itu “berbeda” karena cahayanya belok.
Baca juga: Avengers Infinity War dan Mengapa Butuh Kostum Baru Spiderman
Pembiasan cahaya pada sendok yang masuk ke dalam air (sumber: worldartsme.com)
Teropong bintang, membelokkan cahaya yang ada di sekitar, mengumpulkannya, dan mengirimnya ke mata kita. Alhasil, planet dan berbagai benda angkasa lain bisa keliatan, deh.
Teropong bintang membelokkan cahaya (sumber: giphy.com)
Penggunaan teropong bintang ini bisa dilakukan saat mata berakomodasi maksimum dan saat mata tidak berakomodasi. Kita coba bahas satu per satu ya.
Mata Berakomodasi Maksimum
(Sumber: fisikabc.com)
Mata berakomodasi maksimum maksudnya adalah kondisi kita melihat teleskop dengan menggunakan mata yang terbuka lebar. Pandangan fokus. Dan konsentrasi tinggi. Kalau dalam serial Naruto, mungkin bakal begini nih. :p
(sumber: giphy.com)
Saat mata berakomodasi maksimum, syaratnya ada dua:
1. Sob = tak terhingga
2. S’ok = -Sn
Sob = jarak benda ke lensa objektif
S’ok = jarak bayangan ke lensa okuler
Sn = jarak baca normal (biasanya di soal 25-30cm)
Akibat Sob = tak hingga, maka:
fob = titik fokus lensa objektif
Di teropong bintang, pasti ada yang namanya perbesaran lensa. Hal itu bisa kita dapatkan dengan:
M = Perbesaran teropong bintang
α = Sudut pengamat ke bintang tanpa teropong (o)
Β = Sudut pengamat ke bintang dengan teropong (o)
Persamaan ini bisa kita sederhanakan menjadi;
h = tinggi objek (m)
Karena S’ob = fob, maka;
Lalu, bagaimana cara untuk mencari panjang teleskop? Bisa kita temukan dengan menggunakan rumus berikut:
Karena S’ob = fob, maka hal ini juga berarti:
d = panjang teropong bintang (m)
S’ob = Jarak bayangan ke lensa objektif
Sok = Jarak benda ke lensa okuler
Mata Tidak Berakomodasi
(Sumber: fisikabc.com)
Kondisi mata tidak berakomodasi adalah saat di mana pandangan mata kita tidak berada dalam kondisi “penuh konsentrasi”. Untuk penghitungan rumusnya, terdapat dua syarat juga:
1. S’ok = tak hingga
2. S’ob = fob
fob = titik fokus lensa objektif
S’ob = jarak bayangan ke lensa objektif
Dari kedua syarat itu, kita dapat turunkan rumusnya menjadi:
Karena S’ok tak hingga, maka;
Lalu, untuk penghitungan perbesaran lensa teleskopnya;
Karena S’ob = fob, maka;
Di sisi lain, cara untuk menghitung panjang teleskop adalah
Karena S’ob = fob (dari syarat) dan Sok = fok (dari penurunan rumus), maka;
Nah, sekarang sudah tahu, kan, bagaimana cara teropong bintang bekerja? Kenapa pandangan mata kita terbatas, dan bagaimana cara untuk memperbesarnya. Kalau kamu tertarik dalam pembahasan mengenai rumus-rumus yang ada di dalamnya, langsung aja tonton penjelasan lengkapnya di ruangbelajar! Selain mendapat penjelasan, kamu juga akan mendapat rangkuman infografik mengenai materi ini, lengkap dengan latihan soalnya, lho!
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<h1 class="content-title">
Cara Kerja Teropong Bintang dan Rumus Penghitungannya | Fisika Kelas 11 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kresnoadi" class="">Kresnoadi</a> </p>
<p class="content-info"><span>May 9, 2018 • </span> <span>5 minutes read</span></p>
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<p><img fetchpriority="high" decoding="async" style="width: 821px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Header%20blog%20RG/Fisika_11.jpg" alt="Fisika kelas 11 materi tentang teropong bintang" width="821" height="410" /></p>
<p style="text-align: justify;">Coba deh kamu pergi ke lapangan luas, lalu lihat ke sekitar. Seberapa jauh kamu bisa memandang? Ketika kamu melihat pohon di kejauhan, pasti akan kelihatan sangat keciiiiil. Eh, begitu kamu <em>deketin</em> pohonnya, ternyata ukurannya besar. Kok bisa gitu ya? Hal ini, disebabkan oleh perspektif.</p>
<p><span id="more-9904"></span></p>
<p style="text-align: justify;">Lalu, sekarang coba, deh, kamu tengok ke langit.</p>
<p style="text-align: justify;">Apa yang kamu lihat?</p>
<p style="text-align: justify;">Kalo yang kamu liat jemuran warga, geseran dikit dong.</p>
<p><img decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/jemuran.jpg" alt="jemuran" width="600" height="300" /></p>
<p style="text-align: center;">Jemuran (sumber: merdeka.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Saat kita menatap langit, apalagi di malam hari, pasti hanya terlihat cahaya titik-titik putih. Sama halnya dengan perspektif tadi, titik putih yang sangat kecil ini, ternyata ukuran aslinya besaaar banget. Nah, titik-titik kecil di langit itu, sebenarnya bisa kita lihat dengan alat bantu. Namanya, teleskop atau teropong bintang.</p>
<p style="text-align: justify;">Teropong bintang biasanya digunakan oleh para astronomer untuk mencari planet baru. Di alat ini, terdapat <strong>dua buah lensa cembung</strong>, yaitu <strong>lensa objektif</strong> yang berada di depan, <strong>yang menerima cahaya</strong> langsung dari objek. Dan <strong>lensa okuler</strong>, yaitu lensa yang <strong>berada dekat dengan pengamat.</strong></p>
<p><strong><img decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bagiann%20bagian%20teropong%20bintang.png" alt="bagian bagian teropong bintang" width="600" height="500" /></strong></p>
<p style="text-align: justify;">
<p style="text-align: justify;"><span style="background-color: transparent;">Cara kerja teropong bintang adalah dengan metode “pengumpulan cahaya”. Sekarang bayangkan di rumah kamu sedang turun hujan. Lalu, kamu ambil ember dan tampung air hujannya. Pasti, deh, semakin besar ember yang kamu pakai, air yang kamu tampung juga semakin banyak. </span><em style="background-color: transparent;">Nah, </em><span style="background-color: transparent;">prinsip kerja teropong bintang kurang lebih kayak gitu. Tapi yang ditampung bukan air, melainkan cahaya.</span></p>
<p style="text-align: justify;">
<p><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/menampung%20air%20hujan.gif" alt="menampung air hujan" width="600" height="338" /></p>
<p style="text-align: center;">Tampungan air hujan seperti cara mata dan teropong bintang bekerja (sumber:giphy.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Oke, kalau masih bingung. Kita mundur sedikit mengenai <a href="/bagian-bagian-mata" rel="noopener"><strong>cara mata kita bekerja</strong></a>. Sejatinya, mata kita sama kayak “ember” yang menampung air hujan tadi. Bedanya, si air adalah “cahaya” yang ada di sekeliling kita dan ember yang menampung cahayanya adalah pupil mata kita. Cahaya-cahaya yang masuk ke dalam pupil, pada akhirnya <em>ngebuat</em> kita bisa melihat sekitar.</p>
<p><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/pupil.gif" alt="pupil mata" width="600" height="337" /></p>
<p style="text-align: center;">Pupil mata (sumber: gihpy.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Masalahnya, karena ukuran pupil mata kita kecil, cahaya yang masuk hanya sedikit.</p>
<p style="text-align: justify;">Teropong bintang, membantu kita mengumpulkan cahaya-cahaya yang tidak jatuh ke mata kita, memfokuskannya, dan mengarahkannya langsung ke mata.</p>
<p style="text-align: justify;">Anggap “ember penangkap cahaya” itu diberi lorong, dan di sana, cahaya-cahaya itu dikumpulkan, difokuskan, dan dikirim langsung menuju ke mata kita. Banyaknya jumlah cahaya yang dikumpulkan, tergantung dari area lensa teropong bintang yang kita lihat. Itu artinya, kalau kamu mengubah diameter teropong bintangnya menjadi dua kali lipat lebih besar, kita bakalan dapet cahaya sebanyak 4 kali lipat lebih banyak.</p>
<h2 style="text-align: justify; font-size: 24px;">Bagaimana Teropong Bintang Bisa Mengumpulkan Cahaya?</h2>
<p style="text-align: justify;">Oke, sekarang bagaimana caranya si teropong bintang mengumpulkan cahaya supaya bisa masuk ke pupil mata kita? Bukan. Kamu jangan bayangin teropong bintang ini memungut cahaya kayak orang <em>mungut</em> recehan di jalan. Tetapi, membengkokkan cahaya yang ada di sekitar, dan mengarahkannya ke dalam teropong bintang.</p>
<p style="text-align: justify;">
<p><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rebutan%20receh.gif" alt="rebutan receh" width="600" height="338" /></p>
<p style="text-align: center;">Mengumpulkan uang receh (sumber: giphy.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Cara kerja teropong bintang itu <strong>mengubah arah cahaya dari suatu benda.</strong> Ya, cahaya selalu akan “berubah” arah apabila pindah dari satu medium ke medium lain. Itu lah kenapa kalau kamu memasukkan sendok ke dalam air, mata kita melihat seolah si sendok itu “patah” atau bengkok. Sendoknya <em>gakpapa</em>, tapi cahaya yang kita lihat bengkok, sehingga membentuk gambaran di kepala kita bahwa sendok yang ada di air itu “berbeda” karena cahayanya belok.</p>
<p style="text-align: justify;"> <strong>Baca juga:</strong> <a href="/kostum-baru-spiderman" rel="noopener"><strong>Avengers Infinity War dan Mengapa Butuh Kostum Baru Spiderman</strong></a></p>
<p><img loading="lazy" decoding="async" style="width: 450px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/pensil%20bias.jpg" alt="pensil bias" width="450" height="574" /></p>
<p style="text-align: center;">Pembiasan cahaya pada sendok yang masuk ke dalam air (sumber: worldartsme.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Teropong bintang, membelokkan cahaya yang ada di sekitar, mengumpulkannya, dan mengirimnya ke mata kita. Alhasil, planet dan berbagai benda angkasa lain bisa keliatan, <em>deh</em>.</p>
<p style="text-align: justify;">
<p style="text-align: justify;"><strong><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/lensa%20objektif.gif" alt="lensa objektif" width="600" height="338" /></strong></p>
<p style="text-align: center;">Teropong bintang membelokkan cahaya (sumber: giphy.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Penggunaan teropong bintang ini bisa dilakukan saat mata berakomodasi maksimum dan saat mata tidak berakomodasi. Kita coba bahas satu per satu ya.</p>
<h2 style="text-align: justify; font-size: 24px;"><span style="color: #3366ff;"><strong>Mata Berakomodasi Maksimum</strong></span></h2>
<p><span style="color: #3366ff;"><strong><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/pengamat%20dengan%20mata%20maksimum.jpg" alt="pengamat dengan mata maksimum" width="600" height="340" /></strong></span></p>
<p style="text-align: center;">(Sumber: fisikabc.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Mata berakomodasi maksimum maksudnya adalah kondisi kita melihat teleskop dengan menggunakan mata yang terbuka lebar. Pandangan fokus. Dan konsentrasi tinggi. Kalau dalam serial Naruto, mungkin bakal begini nih. :p</p>
<p><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/mata%20berakomodasi%20maksimum.gif" alt="mata berakomodasi maksimum" width="600" height="449" /></p>
<p style="text-align: center;">(sumber: giphy.com)</p>
<p style="text-align: justify;">Saat mata berakomodasi maksimum, syaratnya ada dua:</p>
<p style="text-align: justify;">
<p style="text-align: justify;"><strong>1. Sob = tak terhingga</strong></p>
<p style="text-align: justify;"><strong>2. S’ok = -Sn</strong></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Sob = jarak benda ke lensa objektif</p>
<p style="text-align: justify;">S’ok = jarak bayangan ke lensa okuler</p>
<p style="text-align: justify;">Sn = jarak baca normal (biasanya di soal 25-30cm)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Akibat Sob = tak hingga, maka:</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 268px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/penurunan%20rumus%20mata%20berakomodasi%20maksimum.jpg" alt="penurunan rumus mata berakomodasi maksimum" width="268" height="315" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">fob = titik fokus lensa objektif</p>
<p style="text-align: justify;">Di teropong bintang, pasti ada yang namanya perbesaran lensa. Hal itu bisa kita dapatkan dengan:</p>
<p style="text-align: justify;">
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="width: 150px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20perbesaran%20lensa%20mata%20berakomodasi%20maksimum.jpg" alt="rumus perbesaran lensa mata berakomodasi maksimum" width="150" height="82" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">M = Perbesaran teropong bintang</p>
<p style="text-align: justify;">α = Sudut pengamat ke bintang tanpa teropong (<sup>o</sup>)</p>
<p style="text-align: justify;">Β = Sudut pengamat ke bintang dengan teropong (<sup>o</sup>)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Persamaan ini bisa kita sederhanakan menjadi;</p>
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="width: 250px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/perbesaran%20lensa%20mata%20berakomodasi%20maksimum.jpg" alt="perbesaran lensa mata berakomodasi maksimum" width="250" height="110" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">h = tinggi objek (m)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Karena S’ob = fob, maka;</p>
<p style="text-align: justify;">
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="width: 150px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20perbesaran%20teropong%20bintang%20mata%20berakomodasi%20maksimum.jpg" alt="rumus perbesaran teropong bintang mata berakomodasi maksimum" width="150" height="94" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Lalu, bagaimana cara untuk mencari panjang teleskop? Bisa kita temukan dengan menggunakan rumus berikut:</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 200px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/panjang%20teleskop%20mata%20berakomodasi.jpg" alt="panjang teleskop mata berakomodasi" width="200" height="41" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Karena S’ob = fob, maka hal ini juga berarti:</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 200px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/panjang%20teleskop%20mata%20berakomodasi%20maksimum.jpg" alt="panjang teleskop mata berakomodasi maksimum" width="200" height="41" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">d = panjang teropong bintang (m)</p>
<p style="text-align: justify;">S’ob = Jarak bayangan ke lensa objektif</p>
<p style="text-align: justify;">Sok = Jarak benda ke lensa okuler</p>
<p style="text-align: justify;">
<h2 style="text-align: justify; font-size: 24px;"><span style="color: #3366ff;"><strong>Mata Tidak Berakomodasi</strong></span></h2>
<p><span style="color: #3366ff;"><strong><img loading="lazy" decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/mata%20tidak%20berakomodasi.jpg" alt="mata tidak berakomodasi" width="600" height="306" /></strong></span></p>
<p style="text-align: center;">(Sumber: fisikabc.com)</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Kondisi mata tidak berakomodasi adalah saat di mana pandangan mata kita tidak berada dalam kondisi “penuh konsentrasi”. Untuk penghitungan rumusnya, terdapat dua syarat juga:</p>
<p style="text-align: justify;">
<p style="text-align: justify;"><strong>1. S’ok = tak hingga</strong></p>
<p style="text-align: justify;"><strong>2. S’ob = fob</strong></p>
<p style="text-align: justify;">
<p style="text-align: justify;">fob = titik fokus lensa objektif</p>
<p style="text-align: justify;">S’ob = jarak bayangan ke lensa objektif</p>
<p style="text-align: justify;">
<p style="text-align: justify;">Dari kedua syarat itu, kita dapat turunkan rumusnya menjadi:</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 200px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20teropong%20bintang%20mata%20tidak%20berakomodasi.jpg" alt="rumus teropong bintang mata tidak berakomodasi" width="200" height="74" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Karena S’ok tak hingga, maka;</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 150px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/turunan%20rumus%20mata%20tidak%20berakomodasi.jpg" alt="turunan rumus mata tidak berakomodasi" width="150" height="189" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Lalu, untuk penghitungan perbesaran lensa teleskopnya;</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 150px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/perbesaran%20lensa%20mata%20tidak%20berakomodasi.jpg" alt="perbesaran lensa mata tidak berakomodasi" width="150" height="93" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Karena S’ob = fob, maka;</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 150px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20perbesaran%20teropong%20bintang%20mata%20berakomodasi%20maksimum-1.jpg" alt="rumus perbesaran teropong bintang mata berakomodasi maksimum-1" width="150" height="94" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Di sisi lain, cara untuk menghitung panjang teleskop adalah</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 200px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/panjang%20lensa%20mata%20tidak%20akomodasi.jpg" alt="panjang lensa mata tidak akomodasi" width="200" height="41" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Karena S’ob = fob (dari syarat) dan Sok = fok (dari penurunan rumus), maka;</p>
<p style="text-align: justify;"> <img loading="lazy" decoding="async" style="width: 175px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/panjang%20lensa%20mata%20tidak%20berakomodasi%20sempurna.jpg" alt="panjang lensa mata tidak berakomodasi sempurna" width="175" height="33" /></p>
<p style="text-align: justify;">
<p style="text-align: justify;">Nah, sekarang sudah tahu, kan, bagaimana cara teropong bintang bekerja? Kenapa pandangan mata kita terbatas, dan bagaimana cara untuk memperbesarnya. Kalau kamu tertarik dalam pembahasan mengenai rumus-rumus yang ada di dalamnya, langsung aja tonton penjelasan lengkapnya di <strong><a href="https://ruangguru.com/belajar" target="_blank" rel="noopener">ruangbelajar!</a> </strong>Selain mendapat penjelasan, kamu juga akan mendapat rangkuman infografik mengenai materi ini, lengkap dengan latihan soalnya, <em>lho!</em></p>
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<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>