First slide

Total internal reflection - Ray optics and optical instruments

Question

A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r’, then the critical angle will be

Moderate

A

$\sin^{- 1} (sinr)$
B

$\sin^{- 1} ({tanr}^{'})$
C

$\sin^{- 1} (tani)$
D

$\tan^{- 1} (sini)$

Solution

$_{D} μ_{R} = \frac{sini}{{sinr}^{'}} \Rightarrow_{R} μ_{D} = \frac{{sinr}^{'}}{sini} = \frac{1}{sinC} \Rightarrow sinC = \frac{sini}{\sin (90 - r)} = \frac{sini}{cosr} = \frac{sini}{cosi} (as ∠ i = ∠ r) \Rightarrow sinC = tani \Rightarrow C = \sin^{- 1} (tani)$

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