$A$ ray of light passes through an equilateral prism such that the angle of incidence $(i)$ is equal to the angle of emergence $(e)$. The angle of emergence is equal to $\left(\frac{3}{4}\right)$ of the angle of the prism. The angle of deviation is: (in $^{\circ}$)

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is......$^o$

When a glass prism of refracting angle $60^{\circ}$ is immersed in a liquid, its angle of minimum deviation is $30^{\circ}$. The critical angle of glass with respect to the liquid medium is (in $^{\circ}$)

If a thin prism of glass is dipped into water,then the minimum deviation (with respect to air) of light produced by the prism will be: $\left( {_a{\mu _g} = \frac{3}{2} \text{ and } _a{\mu _w} = \frac{4}{3}} \right)$

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:

An isosceles prism of angle $A=30^{\circ}$ has one of its surfaces silvered. Light rays falling at an angle of incidence $60^{\circ}$ on the other surface retrace their path after reflection from the silvered surface. The refractive index of the prism material is