When white light passes through a prism it is spread out into a rainbow of colors This effect is known as?

Dispersion of light is defined as follows:

Dispersion of light is the splitting of white light into its constituent colors due to the refractive index of the surface and the wavelength of the light.

If the light entering the prism is not of a single colour then the emergent beam also has different colours arranged in a definite order. It is because the light of different colours have different speeds in a medium expect air. The speed of light in a transparent medium decreases with decrease in the wavelength of light.

Newton's Experiment

Sir Issac Newton, while studying the image of a heavenly body formed due to refraction of white light by a lens, found that the image is coloured at it's edges. He thought that the coloured image is due to some defect in the lens. He then repeated the experiment with a carefully polished lens, but the image was still coloured. Newton then thought that the fault is not in the lens, but there is something in the nature of white light itself due to which the image is coloured at its edges. To investigate it further, he performed another experiment with a $prism$.

Newton allowed white light from sun to enter a dark room through a small aperture in a window and placed a glass prism in the path of light rays. The light coming out of the prism was received on a white screen. On the screen a coloured patch like a rainbow was formed which was termed as spectrum .

Dispersion of light through a glass prism

A glass prism is used to disperse white light. The prism is a 5-faced solid, having two triangular bases and three rectangular surfaces that are inclined toward each other.

Light is sent through one of the rectangular faces, which enters the prism and exits through one of the other rectangular faces. Since different colors of light travel at different speeds, the refractive index is different for each color. As a result, when white light passes through the refracting surface of the prism, its components bend into different angles, causing the single beam of light to separate. Then, the different colors of light bend again because of the refraction caused by the second rectangular surface.

In this way, white light gets split into its component colors upon passing through a glass prism.

Polychromatic light enters a rectangular glass prism of thickness $t=2\text{ cm}.$ If the light strikes with incident angle 30∘30^\circ30∘ in air, what is the lateral separation of violet light ($n=1.52$) and red light ($n=1.51?$)

Angle of refraction within the prism

Use Snell's law to find the refraction angles. For both colors, n1=1n_1 = 1n1​=1 and θ1=30∘\theta_1 = 30^\circθ1​=30∘

n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1 = n_2\sin\theta_2n1​sinθ1​=n2​sinθ2​

θ2=sin⁡−1(n1sin⁡θ1n2)\theta_2 = \sin^{-1}(\frac{n_1\sin\theta_1}{n_2})θ2​=sin−1(n2​n1​sinθ1​​)

Violet θ2=19.205∘\theta_2 = 19.205^\circθ2​=19.205∘

Red θ2=19.337∘\theta_2 = 19.337^\circθ2​=19.337∘

Lateral displacement within the material

Each beam will travel a path diagonally through the prism. The angle of refraction forms a right triangle with the thickness and lateral displacement of the light ray.

tan⁡θ2=lateral displacementthickness=ℓt\tan\theta_2 = \frac{\text{lateral displacement}}{\text{thickness}} = \frac{\ell}{t}tanθ2​=thicknesslateral displacement​=tℓ​

ℓ=ttan⁡θ2\ell = t \tan\theta_2ℓ=ttanθ2​

Violet $$\ell =(0.02\text{ m})\tan (19.205)=6.97\text{ mm}$$

Red $$\ell =(0.02\text{ m})\tan (19.337)=7.02\text{ mm}$$

Lateral separation is the difference between the lateral displacements.

$$\Delta \ell =7.02\text{ mm}-6.97\text{ mm}=0.05\text{ mm}=50\mu \text{m}$$

Using glass prism we can disperse only visible light. But still radiations of different wavelengths can be dispersed by different prisms'. The given below problem explains this.