A ray of light is incident normally on one face of $$30$$º $$-$$ $$60$$º $$-$$ $$90$$º prism of refractive index $$53$$, immersed in liquid of refractive index μ as shown in figure. Match List – I with List – II $$Column-IColumn-II$$

Question

A ray of light is incident normally on one face of $$30$$º $$-$$ $$60$$º $$-$$ $$90$$º prism of refractive index $$53$$, immersed in liquid of refractive index  μ as shown in figure. Match List – I with List – II $$Column-IColumn-II$$

Infinity Learn · Accepted Answer

Apply equation of refraction at (I) & (II) for different cases.

$A) C = \sin^{- 1} (\frac{3}{5}) = 37^{\circ}$

$\begin{array}{l} 5 / 3 \times \sin 30^{\circ} = 1 \times \sin e \\ e = \sin^{- 1} 5 / 6 = 56 . 4^{0} \\ δ = 90 + (- 56.4) = 33 . 6^{0} \\ B) C = \sin^{- 1} (\frac{4}{5}) = 53^{0} \end{array}$

$\begin{array}{l} \frac{5}{3} \times \sin 30 = \frac{4}{3} \times \sin e \\ e = \sin^{- 1} (5 / 8) = 38 . 6^{0} \\ δ = 90 - 38.6 = 51 . 4^{\circ} \\ C) \end{array}$

$D) C = \sin^{- 1} (0.9) = 64^{\circ}$

$\begin{array}{l} \frac{5}{3} \times \sin 60^{\circ} = \frac{3}{2} \sin e \\ e = \sin^{- 1} (0.96) = 74^{\circ} \\ δ = 74 - 60 = 14^{\circ} \end{array}$

Column-I	Column-II
A) $μ = 1$	p) Ray will exit from prism at AC
B) $μ = \frac{4}{3}$	q) Ray will exit from prism at BC
C) $μ = \frac{5}{3}$	r) Ray will exit from prism making an angle $\sin^{- 1} (\frac{5}{9})$ with normal
D) $μ = \frac{3}{2}$	s) Ray will suffer a deviation $δ$ such that $0 \leq δ \leq \frac{π}{2}$
	t) Ray will exit from prism making an angle of $\sin^{- 1} (\frac{5}{8})$ with normal

Total internal reflection - Ray optics and optical instruments

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