Physics Question on Ray optics and optical instruments

Question

The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by

Answer 1

Solution

We know that the angle of deviation depends upon the angle of incidence.
θ4=sin−1nsin(θ3)
A+δ=θ1+θ4, which suggests that
A=θ2+θ3
substituting the value of θ4,
δ=θ1+sin−1nsin(θ3)−A
then the value of δ is
δ=θ1+sin⁻¹ nsin(A−sin⁻¹ (sin(θ1/n))) −A
Plot this on the graph. The curve should be continuous and non-linear. Also, minimum deviation takes place at only value 1 of angle incidence.

Therefore, The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by Option C).

The graph between the angle of deviation (δ) and the angle of incidence (i) for a triangular prism is not a simple linear relationship.

It is a non-linear curve that can be represented by a sine function.
The angle of deviation (δ) is the angle between the incident ray and the emergent ray after passing through the prism.
The angle of incidence (i) is the angle between the incident ray and the normal to the surface of the prism.
As the angle of incidence (i) increases, the angle of deviation (δ) also changes.
Initially, the angle of deviation increases slowly with the angle of incidence, but as the angle of incidence increases further, the angle of deviation starts to increase more rapidly.

This non-linear relationship is due to the refraction of light as it passes through the prism. The refractive index of the prism material and the geometry of the prism play a crucial role in determining the angle of deviation for a given angle of incidence.

To accurately represent the graph between δ and i for a triangular prism, a mathematical equation based on the principles of optics and trigonometry is used. The equation involves the refractive index of the prism material, the apex angle of the prism, and the angle of incidence.

Read more from chapter:**Angle of minimum deviation **