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 begin by understanding the refraction through a prism.

The prism is given to have a refractive index \(\mu = \sqrt{3}\), and one internal angle (\(A\)) of the prism is typically \(60^\circ\) for an equilateral prism. We can use the prism formula to find the angle of emergence (\(e\)):

The prism formula is given by:

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

where:

• \(A\) is the angle of the prism.
• \(\delta\) is the angle of deviation.
• \(n\) is the refractive index of the material.

We need additional specific details about angles and deviation to use the above formula directly. Without loss of generality for a common situation, assume minimum deviation \((\delta_m)\), which simplifies calculations, as typically taught.

When \(\delta = \delta_m\), the angle of incidence and angle of emergence are equal, so:

\(i = e\)

For an equilateral prism with \(A = 60^\circ\), and the given condition of minimum deviation:

\(\delta_m = 2i - A\)

Substituting other values, we solve for \(\delta_m\).

At minimum deviation condition, using Snell's Law at the first surface:

\(\sin i = \mu \sin r\)

where \(r\) is the angle of refraction:

\(\sin r = \frac{\sin A}{n}\)

For \(A = 60^\circ\), substituting:

\(\sin r = \frac{\sin 60^\circ}{\sqrt{3}} = \frac{\sqrt{3}/2}{\sqrt{3}} = \frac{1}{2}\)

Thus, \(r = 30^\circ\).

Using this, and given symmetry at minimum deviation:

The angle of emergence \(e = i = 60^\circ\), derived from standard prism conditions and formulas.

Therefore, the correct answer is:

60°