Question

Find the value of the angle of emergence from the prism. The refractive index of the glass is \(\sqrt3\)

• A. 90°
• B. 60°
• C. 30°
• D. 45°

Answer 1

The Correct Option is B

To find the angle of emergence from the prism, we use the principles of refraction and the prism formula. The relevant formula is the prism formula, which relates the angle of incidence \(i\), the angle of emergence \(e\), the angle of the prism \(A\), and the refractive index \(\mu\) of the material.

The formula for refraction at two surfaces is:

\(\mu = \frac{\sin(\frac{A + \delta}{2})}{\sin(\frac{A}{2})}\) 

Given:

• Refractive Index, \(\mu = \sqrt{3}\)
• Angle of the prism, \(A = 60^\circ\)

Since the refractive index is given as \(\sqrt{3}\), the minimum deviation \( \delta \) needs to be found when light passes symmetrically through the prism:

\(\sqrt{3} = \frac{\sin(\frac{60 + \delta}{2})}{\sin(30)}\)

Since \(\sin(30^\circ) = \frac{1}{2}\), the equation becomes:

\(\sqrt{3} = 2 \sin(\frac{60 + \delta}{2})\)

Simplifying gives:

\(\sin(\frac{60 + \delta}{2}) = \frac{\sqrt{3}}{2}\)

Thus, \(\frac{60 + \delta}{2} = 60^\circ\)

Solving for \(\delta\), we get:

\(\delta = 60^\circ\)

In symmetric passage, angle of incidence \(i\) is equal to angle of emergence \(e\), so:

\(e = \frac{(A + \delta) - A}{2}\)

Thus:

\(e = \frac{(60 + 60) - 60}{2} = 60^\circ\)

Therefore, the angle of emergence from the prism is 60°.