MHT CET · Physics · Ray Optics
Light travels from an optically denser medium 'A' into the optically rarer medium \({ }^{\prime} \mathrm{B}^{\prime}\) with speeds \(1 \cdot 8 \times 10^{8} \mathrm{~m} / \mathrm{s}\) and \(2-7 \times 10^{8} \mathrm{~m} / \mathrm{s}\) respectively. The critical angle
between them is \(\left(\mu_{1}\right.\) and \(\mu_{2}\) are the refractive indices of media \(\mathrm{A}\) and \(\mathrm{B}\)
respectively.)
- A \(\sin ^{-1}\left(\frac{2}{3}\right)\)
- B \(\sin ^{-1}\left(\frac{3}{4}\right)\)
- C \(\tan ^{-1}\left(\frac{2}{3}\right)\)
- D \(\tan ^{-1}\left(\frac{3}{4}\right)\)
Answer & Solution
Correct Answer
(A) \(\sin ^{-1}\left(\frac{2}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{\mu_{\mathrm{A}}}{\mu_{\mathrm{B}}}={ }_{\mathrm{B}} \mu_{\mathrm{A}}=\frac{\mathrm{V}_{\mathrm{B}}}{\mathrm{V}_{\mathrm{A}}}=\frac{2.7 \times 10^{8}}{1.8 \times 10^{8}}=\frac{3}{2}\)
\({ }_{\mathrm{B}} \mu_{\mathrm{A}}=\frac{1}{\sin \mathrm{C}}\)
\(\therefore \frac{3}{2}=\frac{1}{\sin \mathrm{C}}\)
\(\therefore \sin \mathrm{C}=\frac{2}{3}\)
or \(\mathrm{C}=\sin ^{-1} \frac{2}{3}\)
\({ }_{\mathrm{B}} \mu_{\mathrm{A}}=\frac{1}{\sin \mathrm{C}}\)
\(\therefore \frac{3}{2}=\frac{1}{\sin \mathrm{C}}\)
\(\therefore \sin \mathrm{C}=\frac{2}{3}\)
or \(\mathrm{C}=\sin ^{-1} \frac{2}{3}\)
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