MHT CET · Physics · Ray Optics
If angle of incidence is twice the angle of refraction in a medium of refractive index \(\mu\), then angle of incidence is
- A \(2 \cos ^{-1} \frac{\mu}{2}\)
- B \(2 \sin ^{-1} \frac{\mu}{2}\)
- C \(2 \cos ^{-1} \mu\)
- D \(2 \sin ^{-1} \mu\)
Answer & Solution
Correct Answer
(A) \(2 \cos ^{-1} \frac{\mu}{2}\)
Step-by-step Solution
Detailed explanation
According to Snell's law Refractive index, \(\mu=\frac{\sin i}{\sin r}\)
Given \(i=2 r\)
\(\therefore\) \(
\mu=\frac{\sin 2 r}{\sin r}
\)
or \(\mu=\frac{2 \sin r \cos r}{\sin r}\)
or \(\quad \cos ^{-1} \frac{\mu}{2}=r\)
\(
i=2 \cos ^{-1} \frac{\mu}{2}
\)
Given \(i=2 r\)
\(\therefore\) \(
\mu=\frac{\sin 2 r}{\sin r}
\)
or \(\mu=\frac{2 \sin r \cos r}{\sin r}\)
or \(\quad \cos ^{-1} \frac{\mu}{2}=r\)
\(
i=2 \cos ^{-1} \frac{\mu}{2}
\)
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