Question

Draw a ray diagram to  show the refraction of light through a glass prism. Derive the formula for the determination of refractive index of the material of the prism.

Answer 1

Refraction through a prism

PQ → incident ray, QS → refracted ray

ST → emergent ray

The refracted ray QS is incident on the face AC at an angle r₂.The refraction now takes place from glass to air. The ray bends away from the normal  on entering air. ST is the emergent ray and 'd' is the angle of emergence.

The ray PQ would have proceeded straight long PQLK in the absence of the prism. But due to refraction by prism. the travels along S.T. Thus, the ray is deviated through and angle σ.This angle is called angle of deviation.

Now LLQS = i - r, ∠CSQ = e - r_2.

σ is the.exterior angle of ΔLQS.Since exterior angle of a Δ is equal to sum of interior opposite angles.

σ = i - r, + e - r₂ = i + e -(r₁ + r₂)....(i)

Considering quadrilateral AQNS,

When the prism is placed in the minimum deviation position, then