An isosceles glass prism $\left( \mu = \frac{3}{2} \right)$ has one of its equal faces coated with silver. $A$ ray is normally incident on the other face and is reflected twice and then emerges through the base of the prism perpendicular to it,as shown in the figure. Find the angle $\theta$ of the prism in degrees. (in $^{\circ}$)

For an isosceles prism of angle $A$ and refractive index $\mu$,it is found that the angle of minimum deviation $\delta_m=A$. Which of the following options is/are correct?
[$A$] At minimum deviation,the incident angle $i_1$ and the refracting angle $r_1$ at the first refracting surface are related by $r_1=\left(i_1 / 2\right)$.
[$B$] For this prism the refractive index $\mu$ and the angle of prism $A$ are related as $A=\frac{1}{2} \cos ^{-1}(\mu / 2)$.
[$C$] For this prism,the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is $i_1=\sin ^{-1}\left[\sin A \sqrt{4 \cos ^2 \frac{A}{2}-1}-\cos A\right]$.
[$D$] For the angle of incidence $i_1=A$,the ray inside the prism is parallel to the base of the prism.

By placing the prism in the minimum deviation position,the images of the spectrum:

$A$ thin prism $P_1$ with angle $4^o$ made of glass of refractive index $1.54$ is combined with another thin prism $P_2$ made of glass of refractive index $1.72$ to produce no deviation. The angle of prism $P_2$ is.....$^o$

$A$ monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is $\sqrt{3}$,then the angle of incidence is ... $^o$.

The angle of deviation produced by a thin prism when placed in air is $\delta_1$ and that when immersed in water is $\delta_2$. The refractive indices of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. The ratio $\delta_1 : \delta_2$ is