Question

Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt{3}$.

• A. $60^{\circ}$
• B. $30^{\circ}$
• C. $45^{\circ}$
• D. $90^{\circ}$

Answer 1

The Correct Option is A

To find the angle of emergence from the prism, we need to use the prism formula and some basic principles of refraction. The problem involves a prism, and we are given the refractive index of the glass (\( \mu = \sqrt{3} \)).

We can assume that the prism is an equilateral prism, which means its apex angle \( A = 60^{\circ} \). The formula for the angle of deviation \( \delta \) in a prism is given by:

\(\delta = i_1 + i_2 - A\)

Here, \( i_1 \) and \( i_2 \) are the angles of incidence and emergence, respectively. Since the light is passing symmetrically, \( i_1 = i_2 \). The refractive index of the prism \( \mu = \frac{\sin i_1}{\sin r}\), where \( r \) is the angle of refraction.

Now, for minimum deviation condition, \( i_1 = i_2 \) and therefore \( r = \frac{A}{2} = \frac{60^{\circ}}{2} = 30^{\circ} \). Using Snell's Law:

\(\mu = \frac{\sin i}{\sin r} = \frac{\sin i}{\sin 30^\circ} = \frac{\sin i}{0.5}\)

Substituting the given refractive index:

\(\sqrt{3} = \frac{\sin i}{0.5} \Rightarrow \sin i = \sqrt{3} \times 0.5 = \frac{\sqrt{3}}{2}\)

This implies:

i = 60^{\circ}

Since the angle of emergence \( i_2 = i_1 \), the angle of emergence is \( 60^{\circ} \).

Therefore, the correct answer is $60^{\circ}$.

Options Analysis:

• $60^{\circ}$ - Correct, as derived.
• $30^{\circ}$ - Incorrect, possibly confused with angle of refraction.
• $45^{\circ}$ - Incorrect, does not align with any part of the calculations.
• $90^{\circ}$ - Incorrect, not plausible for prism emergence angle.