Process of Refraction of Light Through a Glass Prism​

Let us explain refraction of light through a glass prism in a step-by-step manner:

• The incident light ray will strike the surface AB of the prism at an angle labelled as i, or the angle of incidence.
• As soon as the incident light ray enters the prism,refraction will take place and light will bend towards the normal since it is coming from a rarer medium (air) to denser medium (glass). 
• Here, as evident in the image, the angle between incident ray and normal will be known as the angle of incidence. 
• The angle between refracted ray and normal drawn within the prism, will be known as the angle of refraction (r).
• Now the light is travelling through the prism, bending at angle r. 
• This path of refracted light ray within the prism will depend on both the refractive index of glass and angle of incidence.
• As soon as the refracted ray touches the second surface AC of this prism, it travels back into the air. This ray will be known as an emergent ray. It is basically moving from glass to air.
• Since the refracted ray is moving from denser to rarer medium, the refracted ray will bend away from the normal. 
• The angle formed between emergent ray and the normal is known as the angle of emergence (e).
• If the incident light is white, prism will disperse this light into its constituent colours. Therefore, white light will emerge as a rainbow.

We have also attached a simulation that you can look at to understand how refraction through a prism takes place.

Let us understand the step-by-step derivation of the refractive index of a prism:

From the above figure, we can tell that 

𝛿 =  𝛿₁ + 𝛿₂

= ( i₁ - r₁) + ( i₂+ r₂) 

= ( i₁ +i₂ ) - ( r₁+ r₂)              - (1) 

As we know by basic geometry rules, the sum of angles in a triangle is 180° which means that 

∠APR + ∠A + ∠AQR = 180°

(90° - r₁) + ∠A + (90° - r₂) = 180°

( r₁+ r₂)  = ∠A                      - (2)

Let us substitute the values of equation 2 in equation 1:

𝛿 = ( i₁ +i₂ ) - ∠A                  - (3)

For the case of minimum deviation

i₁ =i₂ =i

We will now use this equivalence relation in equation 3. 

𝛿 = ( i +i ) - ∠A 

𝛿 = ( 2i ) - ∠A 

i = (𝛿 + ∠A)/2

Since   r₁= r₂ =r, we will modify equation 2 as mentioned below:

(r₁ +r₂) = ∠A

(r + r) = ∠A

2r = ∠A

r = ∠A/2

Therefore, refractive index for a medium of prism for the minimum deviation angle (𝛿𝑚) will be:

$$n = \frac{ \sin \left( \frac{ {\delta }_m + A }{2} \right) }{ \sin \left( \frac{A}{2} \right)}$$
$$\frac{ }{}$$

Knowing this is important for JEE Main exam and NEET exam. As we have seen in the above section, a white light will disperse into a colourful spectrum of light when it passes through a prism. Let us understand why this happens:

• A white light is composed of different colours. Every colour in this white light has a different wavelength and frequency. 
• The light in the prism slows down since glass is denser medium than air. Refractive index of the prism material will be different relative to different wavelights of light. 
• The shorter wavelights bend more than longer wavelengths because there is more change in speed of shorter wavelengths of light.
• As per the Snell's law, angle of refraction depends on the refractive index of medium and wavelength of light.
• Since refractive index differs for every colour, each colour will bend at a different angle while entering and exiting the prism.
• Due to this reason, the white light disperses and splits into its constituent colours to form a spectrum.
• One of the main reasons for the dispersion of white light during refraction through a prism is angle of prism as well. 

Here, we have shared the NCERT Exercise of Class 12th Physics chapters for students who are planning to take their board exams next year.

This lesson has been reviewed by subject matter expert Raghvendra Kumar, who has years of experience in teaching. He has qualified for the AIEEE and GATE exams. He specialises in preparing students for JEE Main and NEET as well as for Class 11 and 12 subjects. As a reviewer at Shiksha, he ensures that content has clarity, correctness and exam readiness of concepts and explanation sets. To further maintain the quality of the content being shared on our website, we have referred to the study material provided by NIOS, NCERT and standard Physics books.

Let us take a look at the frequently asked questions related to refraction through a prism which may even be important for competitive exams like IIT JAM exam and CUET exam: