Refraction through a Prism Explained
A prism is a transparent optical element with flat, polished surfaces at an angle to each other. When light passes through a prism, it refracts at both the
TL;DR: A prism is a transparent optical element with flat, polished surfaces at an angle to each other. When light passes through a prism, it refracts at bot…
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Refraction through a Prism: A prism is a transparent optical element with flat, polished surfaces at an angle to each other. When light passes through a prism, it refracts at both the
Refraction through a Prism Explained Simply
A prism is a transparent optical element with flat, polished surfaces at an angle to each other. When light passes through a prism, it refracts at both the This is a key Physics concept for Class 10.
Structure and Terms
A prism typically has a triangular cross-section with two plane surfaces meeting at an angle called the apex angle (A). The angle between the direction of incident ray and emergent ray is called the angle of deviation (δ). The angle through which the ray is turned inside the prism is related to the prism angle and the angles of incidence and refraction at both surfaces.
Refraction at First Surface
When light hits the first surface of the prism, it refracts according to Snell's law: sin(i) = n sin(r1), where i is angle of incidence, r1 is angle of refraction, and n is refractive index of prism. The refracted ray travels through the prism toward the second surface. The angle r1 depends on the angle of incidence and the refractive index of the prism material.
Refraction at Second Surface
The refracted ray hits the second surface from inside the prism. At this surface, the angle of incidence is r2 (related to the prism angle by A = r1 + r2). The ray refracts again as it exits: n sin(r2) = sin(e), where e is angle of emergence. The emergent ray is parallel to the incident ray if the prism angle is small, but at an angle if the prism angle is significant.
Deviation Formula
The angle of deviation δ is the angle between the incident ray direction and the emergent ray direction. It is given by δ = i + e - A, where i is angle of incidence, e is angle of emergence, and A is prism angle. Minimum deviation occurs when the ray passes symmetrically through the prism (i = e and r1 = r2 = A/2). At minimum deviation: n = sin((A + δ_min)/2) / sin(A/2).
Minimum Deviation
Minimum deviation is the smallest angle through which a ray can be deviated by a prism. It occurs when the path of light through the prism is symmetric, meaning the ray hits both surfaces at equal angles. At minimum deviation, the ray travels parallel to the base of the prism and the path inside makes equal angles with the two surfaces. This condition is useful for precise measurements using spectroscopes.
Critical Angle and Total Internal Reflection
If the angle of incidence at the second surface (r2) exceeds the critical angle, total internal reflection occurs instead of refraction. For light traveling from glass to air, the critical angle is given by sin(θ_c) = 1/n. If total internal reflection occurs, no light emerges from the second surface. This principle is used in prisms designed for beam deflection in optical instruments.
Worked Examples
Example 1. A ray of light is incident at 50° on a prism of refractive index 1.5 and prism angle 60°. Find the angle of refraction at the first surface.
Solution: Given: i = 50°, n = 1.5, A = 60°
Using Snell's law at first surface: sin(i) = n sin(r1)
sin(50°) = 1.5 sin(r1)
0.766 = 1.5 sin(r1)
sin(r1) = 0.766/1.5 = 0.511
r1 = 30.7°
The angle of refraction at the first surface is approximately 30.7°.
Example 2. Light passes symmetrically through a prism of angle 60° made of glass with refractive index 1.5. Find the angle of deviation.
Solution: Given: A = 60°, n = 1.5, ray passes symmetrically (i = e, r1 = r2 = A/2 = 30°)
For symmetric passage, use: n = sin((A + δ_min)/2) / sin(A/2)
1.5 = sin((60 + δ_min)/2) / sin(30°)
1.5 = sin((60 + δ_min)/2) / 0.5
sin((60 + δ_min)/2) = 0.75
(60 + δ_min)/2 = 48.59°
60 + δ_min = 97.18°
δ_min = 37.18°
The angle of minimum deviation is approximately 37.2°.
Example 3. A prism has a critical angle of 42° for total internal reflection. Find its refractive index and the wavelength color that would undergo total internal reflection at the second surface.
Solution: Given: θ_c = 42°
Using sin(θ_c) = 1/n
sin(42°) = 1/n
0.669 = 1/n
n = 1/0.669 = 1.49 ≈ 1.5
The refractive index is approximately 1.5.
For total internal reflection to occur, the ray must hit the second surface at an angle greater than 42°. Violet light bends more due to higher refractive index, so it is more likely to undergo total internal reflection than red light.
Where You See This in Real Life
- Spectroscopes used in Indian physics laboratories use prisms to separate light into its spectrum, allowing identification of elements present in light sources.
- The roof prisms used in Indian binoculars and cameras use total internal reflection to flip and erect the image without using additional lenses.
- Periscopes used in military and nautical applications employ prisms with total internal reflection to change the direction of light by 90 degrees.
- Optical fibers in Indian telecommunications networks use the principle of total internal reflection within the prism-like fiber to transmit light over long distances with minimal loss.
Common Mistakes Students Make
- Confusing angle of deviation with angle of refraction. Deviation is the total change in ray direction; refraction angle is at one surface only.
- Using the wrong formula for deviation. Remember δ = i + e - A, not δ = i + e.
- Not recognizing that minimum deviation gives the best precision for measuring refractive index using a spectroscope.
- Assuming the emergent ray is always parallel to the incident ray. It is only parallel when the prism angle is very small.
Frequently Asked Questions
What happens when light passes through a prism?
Light bends (refracts) twice — on entering and on leaving the prism — and bends towards the base. White light also splits into its seven colours, an effect called dispersion.
What is the angle of deviation in a prism?
The angle of deviation is the angle between the direction of the incident ray and the emergent ray. It depends on the prism’s angle, its material and the angle of incidence.
Why does a prism split white light into colours?
Different colours bend by different amounts (violet bends most, red least) because they travel at slightly different speeds in glass. This spreading of colours is called dispersion.