how the light will pass and what is the angle of emergence
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1 Answer

1. User Answers babundra210
Answer:
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 = [tex]\frac{1}{2}[/tex] ⇒ 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) = [tex]\frac{1}{\sqrt{2} }[/tex] sin(r)
here relative refractive index ,μ = [tex]\frac{1}{\sqrt{2} }[/tex], 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.