Refraction Through Prism

Prism Optics

Prism is a transparent medium bounded by refracting surfaces, such that the incident surface (on which light ray is incidenting) and emergent surface (from which light rays emerges) are plane and non parallel.

Prism Refraction

i → Angle of incidence,

e → Angle of emergence,

A → Angle of prism or refracting angle of prism,

r₁ and r₂ → Angle of refraction,

δ → Angle of deviation

A = r₁ + r₂ and i + e = A + δ

For surface AC µ = sin i/sin r₁; For surface AB 1/µ = sin r₂/sin e

Prism Deviation:

For thin prism δ = (µ –1)A. Also deviation is different for different colour light e.g. µ_R < µ_V so δ_R < δ_V.

µ_Flint > µ_Crown so δ_r > δ_c

(i) Maximum deviation: Condition of maximum deviation is

i = 90^o => r₁ = C, r₂ = A – C

and from Snell's law on emergent surface

e = sin^–1 [sin(A–C)/sin C]

δ_max = π/2 + sin^–1 [sin(A–C)/sin C] – A

(ii) Minimum deviation: It is observed if i = e and r₁ = r₂ = r, deviation produced is minimum.

(a) Refracted ray inside the prism is parallel to the base of the prism for equilateral and isosceles prisms.

(b) r = A/2 and i = A + δ_m/2

(c)  (Prism formula)

Prism Dispersion

The splitting of white light into its constituent colors is called dispersion of light.

Angular dispersion (θ): Angular separation between extreme colours i.e. θ = δ_V – δ_R = (µ_V – µ_R)A. It depends upon µ and A.

Dispersive power (ω): ω = θ/δ_y = µ_V –µ_R/µ_y – 1

            where {µ_y – µ_V+µ_R/2}

=> It depends only upon the material of the prism i.e. m and it doesn't depends upon angle of prism A