Refraction of light through a prism

Refraction of light through a prism :- Consider a monochromatic light ray PQ incident on the face AB of prism ABC of angle of prism A and refractive index μ.

Let

Angle of deviation(δ)

(Refraction of light through a prism)

Angle of deviation(δ): The angle through which the incident ray turns in passing through a prism is called angle of deviation. In the above figure if we extend the emergent ray RS backward then it meets the original direction of incident ray(PQ) at a point T. Here ∠KTR = angle of deviation(δ).

Graph between angle of deviation(δ) and angle of incidence(i)

(Refraction of light through a prism)

The graph of angle of deviation (δ) against the angle of incidence (i) is plotted and it is obtained as shown below :-

The graph of angle of deviation (δ) versus angle of incidence (i) for a prism shows that the deviation initially decreases with increasing angle of incidence, reaches a minimum value (δₘᵢₙ), and then increases again. The shape of the graph forms a curve with a distinct minimum point. Also the graph is not symmetric about the minimum deviation position.

✅ Minimum Deviation (δₘᵢₙ) :

• δₘᵢₙ represents the smallest possible deviation experienced by a light ray passing through the prism.
• At this point, the path of the light ray inside the prism is symmetric relative to the prism’s geometry.
• The corresponding angle of incidence at this condition is denoted by i_m, and the angle of emergence is equal to it (i_₁ = i_₂ = i_ₘ).

✅ Two Angles of Incidence (i_₁ and i_₂) :

• For any deviation greater than δₘᵢₙ, a straight line parallel to the i-axis intersects the graph at two distinct points, corresponding to two different angles of incidence, i_₁ and i_₂​.
• This means that the same deviation occurs at two different angles of incidence.
• These two angles correspond to :

i₁ → the actual angle of incidence of the incoming ray.

i₂ → called the angle of emergence, representing the ray as if it is incident from the opposite direction.

• Principle of Optical Reversibility :
  Due to this principle, light retracing its path backward through the prism would have the same deviation at angle i₂​ as it did at i₁​ during forward passage.

✅ At Minimum Deviation (δₘᵢₙ) :

• The two angles coincide (i₁ = i₂​).
• The light ray travels symmetrically through the prism.