Refraction Through a Prism: Mechanism and Concepts

Refraction refers to a phenomenon where light bends as it passes from one medium to another. When light passes through a glass prism, light refracts both while entering the prism as well as while exiting. The positions of entry and exit (refracting surfaces) are not parallel to each other, so the emergent and incident rays are also not parallel to each other. The ray of light deviates as it passes through the prism. 

Key Takeaways: Refraction, Refractive Index, Prism, Refraction Through Prism, Angle of Deviation, Dispersion of Light, Light, Light rays, Light wave

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Refraction

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Refraction is a physical phenomenon in which light rays bend at the meeting point of two transparent media. This occurs mainly because of change in direction of the light wave and also bending of light waves at the meeting point of the media. The change in direction or bending of the light wave occurs due to change in light wave’s speed when it reaches the new surface and the resulting phenomenon is refraction.

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Refractive Index

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The extent of bend in the light rays when entering into another medium is measured by an index called refractive index. Refractive index is denoted by the alphabet ‘n’.

• ‘n’ is a derived quantity.
• It is the ratio of c and v

Where c= velocity/speed of light of a certain wavelength in the air

 And v= velocity of light in any medium.

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What is a Prism?

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A prism is a solid geometric figure whose end faces are similar in shape and have equal and parallel rectilinear figures. A prism’s sides are always either parallelogram are rectangles. Prisms exist in many shapes such as triangle, square, rectangle etc., Prisms must be made up of transparent material when being used for refraction. The sides of a prism must have an acute angle (less than 90 degrees).

Types of Prisms

 There a few kinds of prisms present they can be seen as:

1. Dispersive prism
2. Reflective prism
3. Beam splitting prism
4. Polarizing prism
5. Deflecting prism

Now that we’ve seen what is a prism and what is refraction individually, let’s see how refraction takes place in a prism.

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Refraction Through a Prism

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Let us consider a glass triangular prism and name it as ABC. Let BC be the base and AB and AC are its two refracting surfaces. From above figure we can see that the line OP is considered as the incident light ray. The light entering the prism is basically the incident ray. Upon reaching the new surface which is of the prism’s side, the light ray’s speed changes and it bends creating a new ray within the prism and this ray is called the refracted ray. Let us call this refracted ray as PQ. The refracted light ray then travels through the prism and comes out of the prism from its other side. The light ray that comes out is called an emergent ray because it emerges out of the surface. In the figure taken, the emergent ray is named as QR. As can be seen, QR the emergent ray bends with an angle from the refracted ray PQ because of the change in medium.

The angle of incidence is taken as ‘i’ and the angle of refraction is taken as ‘r’

• Angle of incidence is the angle at which the light ray enters the medium
• Angle of refraction is the angle at which the light ray is refracted from the original path of the ray.
• Angle of deviation is the angle at which the light ray gets deviated

When light enters the prism, it bends towards it and when it emerges out of the prism, it bends away from it. So, the angle between the incidence and emergence is the angle of deviation. The angle of deviation is denoted with δ. Since here it is a single refraction, the angle of refraction can be written as:

In this case,

where A is the angle between the lateral surfaces of the prism.

Mathematically, ∠A and ∠Q form 180o and the angle of prism of (A) is r₁+r₂

r₁= angle of refraction inside the prism

r₂= angle of refraction outside the prism.

i1= angle of incidence when the light is entering the prism.

i2 = angle of emergence while exiting prism.

For an angle of minimum deviation, i₁= i₂=i

δ min = 2i-A

For small angle between lateral surfaces A,

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Minimum Angle of Deviation for a Prism

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The minimum angle of deviation can be represented as Dm. Dm when minimum, the ray becomes parallel to the base i.e., i=e ⇒ r1 = r2 = r, then r = A/2 and Dm = 2i-A, where i is the angle of emergence, r1 and r2 are the angles of refraction respectively. A is the angle of the prism which is the angle between two adjacent sides of the prism.

What happens in a prism?

In a prism, the main phenomenon that occurs is the “Dispersion of light rays”

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What is Dispersion of Light?

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Dispersion of light is the division or splitting of one light ray into a band of different light rays depending on the different wavelengths, speeds and frequencies.

What causes dispersion?

Dispersion is mainly caused due to change in medium. Dispersion is the amount in which a light ray gets refracted depending on its frequency and wavelength when the light ray changes its medium. When a light ray touches a prism, it gets refracted and when emerging out of the prism medium, it gets dispersed into a band of seven colours commonly known as VIBGYOR or the Rainbow colours.

As can be seen from the picture, the beam of white light gets dispersed and on reaching the other surface it gets further dispersed and causes the rainbow colours VIBGYOR on the white screen placed on the right.

• V-violet
• I-indigo
• B-blue
• G-green
• Y-yellow
• O-orange
•  R-red

The colours have different wavelengths and different speeds and exhibit different properties in various media. Dispersion was discovered by Issac Newton in 1665.

Do you ever wonder how rainbows are formed?

Rainbows are formed when it is raining when the sun is still present. They are formed because the raindrops act as a prism for the white light from the sun and gets dispersed within the raindrop and while leaving the drop from the other end, they cause the spectrum of seven colours and thus a rainbow is formed in the clouds. Rainbows are always formed on the opposite end of the sunshine.

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Things to Remember

• Refraction refers to a phenomenon where light bends as it passes from one medium to another. 
• When light passes through a glass prism, light refracts both while entering the prism as well as while exiting. 
• The extent of bend in the light rays when entering into another medium is measured by an index called refractive index.
• A prism is a solid geometric figure whose end faces are similar in shape and have equal and parallel rectilinear figures. 
• In a prism, the main phenomenon that occurs is the “Dispersion of light rays” 
• The beam of white light gets dispersed and on reaching the other surface it gets further dispersed and causes the rainbow colours VIBGYOR.

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