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: Relative index:
Light goes from the liquid into the glass, so the effective index is $\frac{n_g}{n_\ell}$.

Step 2: Compute:
$\frac{3/2}{1/3} = 4.5$. The ratio of deviations is $\frac{4.5 - 1}{1.5 - 1} = \frac{3.5}{0.5} = 7$. So $\delta_2 = 7\delta_1$ (C).

Final Answer:
$\delta_2 = 7\delta_1$. \[ \boxed{\delta_2 = 7\,\delta_1} \]