Question

A ray of light incident on one face of an equilateral glass prism having refractive index \(\sqrt{2}\), produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is \((sin90^{\circ} = 1)\)
\((sin30^{\circ} = \frac{1}{2})(sin45^{\circ} = \frac{1}{\sqrt{2}})\)

• A. \(sin^{-1}(\sqrt{2}sin15^{\circ})\)
• B. \(sin^{-1}(\frac{1}{\sqrt{2}}sin15^{\circ})\)
• C. \(sin^{-1}(\sqrt{2}sin30^{\circ})\)
• D. \(sin^{-1}(\frac{1}{\sqrt{2}}sin45^{\circ})\)

Hint:

For a thin prism the deviation is (n_rel - 1) A, where n_rel is the index of the prism relative to the surrounding medium.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a thin prism of angle A, the minimum deviation is \(\delta = (n - 1)A\), where n is the refractive index of the prism relative to the surrounding medium.

Step 2: In air:
\(\delta_1 = \left(\frac32 - 1\right)A = \frac A2\).

Step 3: In the liquid (using the values given):
The relative index is \(\frac{n_g}{n_l} = \frac{3/2}{1/3} = \frac92\).
\[ \delta_2 = \left(\frac92 - 1\right)A = \frac72A \]

Step 4: Ratio:
\(\frac{\delta_2}{\delta_1} = \frac{7A/2}{A/2} = 7\), so \(\delta_2 = 7\delta_1\).

Final Answer:
The new deviation is \(7\delta_1\), option (C). \[ \boxed{\delta_2 = 7\,\delta_1} \]