How the light will pass and what is the angle of emergence

The light ray goes inside with angle of refraction 30° and gets reflected at an angle 30° and then comes out refracted at an 45° with normal of third face

Explanation:

At the first face of prism where the light is first incident,

we can use snell's law to determine the angle of refraction

given refractive index of prism , μ'= √2.

and angle if incidence , i = 45°

now from snell's law,   sin(i) = μ sin(r),    r= angle of refraction

                                                                 μ= relative refractive index

⇒ sin45° = √2 sinr

⇒ sinr = ⇒ r = 30°

Now, let top corner of prism's triangular face be A

         point where light is incident be B

         point where light gets reflected on silvered surface be C

so that ABC forms a triangle

now as r = 30°, ∠ABC = 90°-30° = 60°

As sum of angles in a triangle is 180°,

∠ACB = 60° (since ∠BAC = 60°)

⇒ angle of incidence on silvered face = 90°-60°= 30°

⇒ angle of reflection = 30°

Using same theory as above,

the angle of incidence on third face = 30°

Again using snell's law, sin(i) = μ sin(r)

⇒ sin(30) = sin(r)

here relative refractive index ,μ = , since light travels from prism to air

⇒ r= 45°

⇒The light ray goes inside with angle of refraction 30° and gets reflected at an angle 30° and then comes out refracted at an 45° with normal of third face.