Find the value of the angle of emergence from the prism. Refractive index of the glass is √ 3 .

The correct option/answer is 60°.

Based on the standard physics problem details and the accompanying diagram, we are given:
1. A glass prism with a prism angle (angle of the prism) of $A=60°$.
2. A light ray incident on the first refracting face of the prism at an angle of incidence $i=60°$.
3. The refractive index of the glass prism is $\mu =\sqrt{3}$ and the surrounding medium is air with a refractive index of ${\mu }_{\text{air}}=1$.

To find the angle of emergence ($e$), we follow a step-by-step approach using Snell's Law and the geometry of a prism:

Step 1: Apply Snell's Law at the first refracting surface
Snell's Law at the first boundary (air-to-glass interface) is given by:
${\mu }_{\text{air}}·\sin \left(i\right)=\mu ·\sin \left(r_1\right)$
where $r_1$ is the angle of refraction inside the prism.

Substitute the given values into the equation:
$1·\sin (60°)=\sqrt{3}·\sin \left(r_1\right)$
Since $\sin (60°)=\frac{\sqrt{3}}{2}$, we have:
$\frac{\sqrt{3}}{2}=\sqrt{3}·\sin \left(r_1\right)$

Dividing both sides by $\sqrt{3}$:
$\sin \left(r_1\right)=\frac{1}{2}$
This gives the first refraction angle:
$r_1=30°$

Step 2: Use prism geometry to find the angle of incidence at the second surface
For any prism, the relation between the prism angle $A$ and the internal refraction angles $r_1$ and $r_2$ is:
$A=r_1+r_2$
Substitute $A=60°$ and $r_1=30°$:
$60°=30°+r_2$
Solving for $r_2$:
$r_2=30°$

Step 3: Apply Snell's Law at the second refracting surface (glass-to-air interface)
Snell's Law at the boundary where the light ray emerges into the air is:
$\mu ·\sin \left(r_2\right)={\mu }_{\text{air}}·\sin \left(e\right)$
Substitute the values into the equation:
$\sqrt{3}·\sin (30°)=1·\sin \left(e\right)$
Since $\sin (30°)=\frac{1}{2}$:
$\sqrt{3}·\frac{1}{2}=\sin \left(e\right)$
$\sin \left(e\right)=\frac{\sqrt{3}}{2}$

Taking the inverse sine of both sides:
$e=60°$

Thus, the value of the angle of emergence from the prism is 60°.