In the given figure,what is the angle of the prism?

In a thin prism of glass (refractive index $\mu = 1.5$),which of the following relations between the angle of minimum deviation $\delta_m$ and the angle of refraction $r$ is correct?

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 $^{\circ}$)

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

$A$ ray of light incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$, produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is $(\sin 90^{\circ} = 1, \sin 30^{\circ} = 0.5, \sin 45^{\circ} = 1/\sqrt{2})$.

$A$ ray of monochromatic light suffers a minimum deviation of $38^{\circ}$ while passing through a prism of refracting angle $60^{\circ}$. The refractive index of the prism material is: