When white light passes through an achromatic combination of prisms,what is observed?

$A$ ray of light is incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$. It produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is

$A$ prism of refracting angle $60^\circ$ is made with a material of refractive index $\mu$. For a certain wavelength of light,the angle of minimum deviation is $30^\circ$. For this wavelength,the value of the refractive index of the material is:

The angle of deviation through a prism is minimum when
$(A)$ Incident ray and emergent ray are symmetric to the prism
$(B)$ The refracted ray inside the prism becomes parallel to its base
$(C)$ Angle of incidence is equal to that of the angle of emergence
$(D)$ When angle of emergence is double the angle of incidence
Choose the correct answer from the options given below

In the given figure,the face $AC$ of the equilateral prism is immersed in a liquid of refractive index $n$. For an incident angle of $60^{\circ}$ at the side $AC$,the refracted light beam just grazes along the face $AC$. The refractive index of the liquid is $n = \frac{\sqrt{x}}{4}$. The value of $x$ is (Given refractive index of glass $= 1.5$)

$A$ prism of crown glass with a prism angle of $9^{\circ}$ and a prism of flint glass are used to make a direct vision spectroscope. If the refractive indices of crown and flint glass are $1.40$ and $1.60$ respectively,then the refracting angle of the flint glass prism will be.....$^{\circ}$