JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2022
- Medium
- MCQ
Light travels in two media \(M _{1}\) and \(M _{2}\) with speeds \(1.5 \times 10^{8} ms ^{-1}\) and \(2.0 \times 10^{8} ms ^{-1}\) respectively. The critical angle between them is.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\tan ^{-1}\left(\frac{3}{\sqrt{7}}\right)\)
Step-by-step Solution
Detailed explanation
\(V =\frac{ C }{ n }\)
\(n_{d} \sin i_{c}=n_{r} \sin 90^{\circ}\)
\(\sin i_{ C }=\frac{ n _{ r }}{ n _{ d }}=\frac{ V _{ d }}{ V _{ I }}\)
\(\sin i_{c}=\frac{1.5 \times 10^{8}}{2 \times 10^{8}}=\frac{1.5}{2}\)
\(\sin i_{c}=\frac{3}{4}\)
\(\tan i_{c}=\frac{3}{\sqrt{4^{2}-3^{2}}} \Rightarrow \frac{3}{\sqrt{7}}\)
\(i_{c}=\tan ^{-1}\left(\frac{3}{\sqrt{7}}\right)\)
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