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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.

Refraction through a prism

Fig. 26
A = r1 + r2 and i + e = A + δ
For surface 113467.png; for surface AB, 113476.png

Deviation through a prism

For thin prism δ = (μ – 1)A. Also deviation is different for different color light, e.g., μR < μV, so δR < δV.
μflint > μCrown, so δF > δC
  1. Maximum deviation: Condition of maximum deviation is ∠i = 90° ⇒ r1 = C, r2 = AC and from Snell’s law on emergent surface
Fig. 27
  1. Minimum deviation: It is observed if ∠i = ∠e and ∠r1 = ∠r2 = r, deviation produced is minimum.
Fig. 28
  • Refracted ray inside the prism is parallel to the base of the prism for equilateral and isosceles prisms.
  • 113498.png and 113511.png
  • 113519.png or 113525.png(Prism formula)

Condition of no emergence

For no emergence of light, TIR must take place at the second surface
For TIR at second surface, r2 > C, so, A > r1 + C (From A = r1 + r2)
As maximum value of r1 = C, so, A 2C. for any angle of incidence.
If light ray incident normally on first surface, i.e., ∠ i = 0°, it means ∠r1 = 0°. So in this case condition of no emergence from second surface is A > C.
⇒ sin A > sin C sin A > 1/μ μ > cosec A

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