Question

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

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is C

We know that the angle of deviation depends upon the angle of incidence. 
θ₄​=sin⁻¹nsin(θ₃​)
A+δ=θ₁​+θ_4​, which suggests that
A=θ_2​+θ₃​
substituting the value of θ_4,
δ=θ¹​+sin⁻¹nsin(θ₃​)−A
then the value of δ is 
δ=θ_1​+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 

Answer 2

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

 

Real Life Applications

• Minimum deviation occurs when the angle of deviation is minimized due to the angle of the incident. For this phenomenon, the angle of incidence should be equal to the critical angle of the prism.
• A prism spectrometer helps in separating different wavelengths of light.
• Optical fibres help in transmitting light over long distance

All these use the phenomena of minimum deviation. 
 

Question can also be asked as

1. What is the minimum deviation?
2. How does the angle of deviation vary with the angle of incidence for a triangular prism?
3. What is the shape of the graph between the angle of deviation and the angle of incidence for a triangular prism?

Answer 3

The correct answer is Option C) 

Prism formula 

The Prism formula is derived by using Snell's law. The main principle is based on the bending of light when it passes through the prism. Prism is polished flat and transparent and it reflects light. There are various types of prism as mentioned below. 

Type of prism

Based on the properties and uses, prism can be classified as follows:

• Dispersion Prism
• Reflection Prism
• Deflection Prism
• Polarising Prism
• Beam splitting Prism

Reflection through prism

Light will bend when it passes from one medium to another, it is called reflection through prism. 

• On bending the white light splits into seven colours.
• This is due to differences in the refractive index.
• The bending of light is due to the difference in their wavelength.

Read more: Dispersion without deviation