Calculate the angle of minimum deviation for an equilateral triangular prism of refractive index $\sqrt{3}$. (in $^{\circ}$)

At the condition of minimum deviation,the angle of emergence is .......

If the angle of a prism is $60^{\circ}$ and the angle of minimum deviation is $40^{\circ}$,then the angle of refraction will be (in $^{\circ}$)

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{\circ}$. One of the two refracting surfaces of the prism is made a mirror inwards,by silver coating. $A$ beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is (in $^{\circ}$)

An isosceles glass prism with base angles $40^{\circ}$ is clamped over a tray of water in a position such that the base is just dipped in water. $A$ ray of light incident normally on the inclined face suffers total internal reflection at the base. If the refractive index of water is $1.33$,then the condition imposed on the refractive index $\mu$ of the glass is

$A$ thin prism $P_1$ with angle $6^{\circ}$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ will be