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Physics Question on Ray optics and optical instruments

If angle of incidence is twice the angle of refraction in a medium of refractive index μ\mu , then angle of incidence is

A

2 cos−1μ22 \,cos ^{-1} \frac{\mu}{2}

B

2 sin−1μ22 \,sin ^{-1} \frac{\mu}{2}

C

2 cos−1μ2\, cos^{-1} \mu

D

2 sin−1μ2\, sin ^{-1} \mu

Answer

2 cos−1μ22 \,cos ^{-1} \frac{\mu}{2}

Explanation

Solution

According to Snell's law
Refractive index,   μ=sin⁡ isin⁡ r\, \, \mu=\frac{\sin\, i}{\sin\, r}
Given, i=2ri = 2r
∴μ=sin⁡ 2rsin⁡ r\therefore \mu=\frac{\sin\, 2r}{\sin\, r}
or μ=2sin⁡ rcos rsin⁡ r\mu=\frac{2\sin\, rcos\, r}{\sin\, r}
or cos⁡−1μ2=r\cos^{-1} \frac{\mu}{2}= r
⇒i=2cos⁡−1μ2\Rightarrow i = 2 \cos^{-1}\frac{\mu}{2}