A glass prism with a refracting angle of $60^{o}$ has a RI of 1.52 for red and 1.6 for violet light. A parallel beam of white light is incident on one face at an angle of incidence, which gives minimum deviation for red light. For this situation mark the correct statement(s)
Use $- [\sin ({49.7}^{\circ}) = 0.760, \sin ({31.6}^{\circ}) = 0.520$ , $\sin ({28.4}^{\circ}) = 0.475 \sin 56^{\circ} = 0.832]$

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The angle of incidence is 31.6°

The angular dispersion produced by the prism is 28.4°

The angle of incidence is 49.7°

The angular dispersion produced by the prism is 6.3°

answer is B, D.

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Detailed Solution

For red light, $\sin (\frac{A + δ_{m}}{2}) = μ \sin \frac{A}{2}$

$\begin{array}{l} \Rightarrow \sin (\frac{60 + δ_{m}}{2}) = 1.52 \sin 30^{\circ} \\ \Rightarrow \sin (\frac{60 + δ_{m}}{2}) = 0.760 = \sin ({49.7}^{\circ}) \end{array}$

$\Rightarrow δ_{m} = 2 \times 49.7 - 60 = {39.4}^{0}$

From $δ_{m} = 2 i - A$

$\Rightarrow i = \frac{δ_{m} + A}{2} = {49.7}^{0}$

For violet light,

$\begin{array}{l} \frac{\sin i}{\sin r_{1}} = \frac{1.60}{1} \Rightarrow \sin r_{1} = \frac{\sin ({49.7}^{\circ})}{1.6} = 0.475 \\ \Rightarrow r_{1} = {28.4}^{\circ} \end{array}$

So, $r_{2} = 60 - 28.4 = {31.6}^{0}$

$\begin{array}{l} \frac{\sin {31.6}^{\circ}}{\sin i_{2}} = \frac{1}{1.6} \Rightarrow \sin i_{2} = 0.832 \Rightarrow i_{2} = 56^{\circ} \\ δ_{v} = i + i_{2} - A = {49.7}^{\circ} + 56^{\circ} - 60^{\circ} = {45.7}^{\circ} \\ θ = δ_{v} - δ_{R} = 45.7 - 39.4 = {6.3}^{\circ} \end{array}$