Refractive Index of an Equilateral Prism
A ray of light passes through an equilateral glass prism such that the angle of incidence equals the angle of emergence. The angle of emergence is 3/4 of the angle of the prism. Find the refractive index of the prism.
Step 1: Given Data
e = 3/4 × 60°
e = 45°
Step 2: Use Prism Relation
For a prism:
When i = e (minimum deviation condition):
Step 3: Apply Snell’s Law
Final Answer
Correct Option: (C)
Theory: Minimum Deviation in a Prism
When a ray passes symmetrically through a prism (angle of incidence equals angle of emergence), the prism is said to be in the condition of minimum deviation.
Important Relations
For an equilateral prism, A = 60°. Therefore internal refraction angle becomes 30°.
Frequently Asked Questions
Why is the prism in minimum deviation condition?
Because the angle of incidence equals the angle of emergence, the light path inside the prism is symmetrical.
Why is A equal to 60°?
An equilateral prism has all internal angles equal to 60°.
Why is r equal to A/2?
Under minimum deviation, r₁ = r₂, so each equals half the prism angle.
Which formula gives refractive index?
Snell’s law is applied at the first refracting surface: μ = sin i / sin r.