First slide

Ray optics

Question

A ray of light refracts from medium 1 into a thin layer of medium 2, crosses the layer and is incident at the critical angle on the interface between the medium 2 and 3 as shown in the figure. If the angle of incidence of ray is $θ$ , the value of $θ$ is :

Moderate

A

$\sin^{- 1} (\frac{8}{9})$
B

$\sin^{- 1} (\frac{13}{18})$
C

$\sin^{- 1} (\frac{13}{16})$
D

$\sin^{- 1} (\frac{8}{13})$

Solution

$\frac{μ_{2}}{μ_{1}} = \frac{\sin i}{\sin r}; \frac{1.6}{1.8} = \frac{\sin θ}{\sin r} \sin r = \frac{16}{18} \sin θ; r = c; \frac{1.3}{1.8} = \frac{16}{18} \sin θ θ = \sin^{- 1} (\frac{13}{16})$

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