$A$ parallel beam of light is incident from air at an angle $\alpha$ on the side $PQ$ of a right-angled triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face $PR$ when $\alpha$ has a minimum value of $45^{\circ}$. The angle $\theta$ of the prism is (in $^{\circ}$)

$A$ ray of light is incident normally on one of the faces of a prism of angle $30^\circ$ and refractive index $\sqrt{2}$. The angle of deviation will be.....$^\circ$

One face of a glass prism is silver-polished. $A$ light ray falls at an angle of $45^{\circ}$ on the other face. After refraction,it is subsequently reflected from the silvered face and then retraces its path. The refracting angle of the prism is $30^{\circ}$. The refractive index of the prism is:

In the visible region,the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega^{\prime}$ and $d, d^{\prime}$ respectively. The condition for obtaining dispersion without deviation,when the two prisms are combined,is:

An achromatic prism is made by combining two prisms $P_1$ $(\mu_v = 1.523, \mu_r = 1.515)$ and $P_2$ $(\mu'_v = 1.666, \mu'_r = 1.650)$,where $\mu$ represents the refractive index. If the angle of the prism $P_1$ is $10^o$,then the angle of the prism $P_2$ will be.....$^o$

$A$ glass prism has a right-triangular cross-section $ABC$,with $\angle A=90^{\circ}$. $A$ ray of light parallel to the hypotenuse $BC$ and incident on the side $AB$ emerges grazing the side $AC$. Another ray,again parallel to the hypotenuse $BC$,incident on the side $AC$ suffers total internal reflection at the side $AB$. Which one of the following must be true about the refractive index $\mu$ of the material of the prism?