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

The correct answer is 60⁰.

Based on the provided image, we can observe the path of the light ray as it travels through the prism. The ray is incident normally (perpendicularly) on the first face of the prism. Because it strikes the surface at a normal, the angle of incidence is $0°$, and the ray enters the prism undeviated. Thus, the first angle of refraction is $r_1=0°$.

The angle of the prism is given as $A=30°$. We know that for a prism, the sum of the internal angles of refraction equals the angle of the prism:

$r_1+r_2=A$

Substituting our known values:

$0°+r_2=30°$

$r_2=30°$

This means the light ray strikes the second face of the prism from the inside at an angle of incidence of $30°$. Now, we can apply Snell's Law at this second interface to find the angle of emergence $e$:

$n_{1}sin\left(r_2\right)=n_{2}sin\left(e\right)$

Here, $n_1$ is the refractive index of the glass prism ($\sqrt{3}$) and $n_2$ is the refractive index of the surrounding air (which is $1$). Plugging these values into the equation yields:

$\sqrt{3}·sin(30°)=1·sin\left(e\right)$

Since $sin(30°)=\frac{1}{2}$, we have:

$\sqrt{3}·\frac{1}{2}=sin\left(e\right)$

$sin\left(e\right)=\frac{\sqrt{3}}{2}$

The angle whose sine is $\frac{\sqrt{3}}{2}$ is $60°$. Therefore, the angle of emergence from the prism is $60°$.