Question

How does the angle of deviation produced by a prism change with increase in the angle of incidence. Draw a curve showing the variation in the angle of deviation with the angle of incidence at a prism surface.

Answer 1

As the angle of incidence increases, the angle of deviation decreases first and reaches to a minimum value (δm) for a certain angle of incidence. By further increasing the angle of incidence, the angle of deviation is found to increase.
Variation of angle of deviation (δ) with angle of incidence(i): 

 

Answer 2

The deviation angle first increases with increasing incidence angle and then decreases. From figure,

δ = δ1 + δ₂                               ....(i)

and i = δ₁ +γ₁ ; e = δ₂ +γ₂  

⇒ i = γ₁ = δ₁                      ....(ii)

⇒ e - γ_{1 =} δ₂                       ....(iii)

from ΔON₁ N₂ 

γ_{1 +}γ₂ + ∠N₁ ON₂=180°            ....(iv)

from cyclic quadrilateral

∠A + ∠N₁ON₂ = 180°                 ....(v)

from (iv) and (v) 

γ_{1 +}γ₂ = A

δ = i - γ₁ + e - γ₂

=( i - e) - (γ₁ + γ2)                    ...(vi)

at δm ; 

i = e ; γ₁ = γ₂₌ γ

δm =2i - A                                          ...(vii)

The variation in the angle of deviation with the angle of incidence at a prism surface

Graph between i and  δ_m