Angle of Deviation in a Prism – Formula, Diagram & Applications

The angle of deviation in a prism is the angle that is formed between the direction of the light that is coming into the prism and the direction of the light that is coming out of the prism.

When light goes into a prism it gets bent because it passes through two surfaces.

This bending of the path is what we call the angle of deviation in a prism.

It is the amount by which the light changes direction from its original straight path.

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Angle of Deviation in Prism Formula and Derivation

To really get what the angle of deviation, in a prism means you have to picture a beam of light going through a triangle shaped piece of glass like a prism. In physics a prism is a piece of glass that we use to bend light.

A prism has least two smooth surfaces that are tilted at a certain angle.

When a light ray, with one color, which is called a light ray hits the first surface of the prism it bends towards the middle as it goes from air into the glass.

The prism bends the ray because it is moving from a thinner material, which is air to a thicker material, which is the glass of the prism. When light hits the face it changes direction and moves away, from the normal as it comes out into the air again. If you keep going with the light ray and the final light ray that comes out and you extend them they will meet at a point. The ray that goes in and the light ray that comes out they intersect at this point. The angle that is created when these two lines intersect is called the angle of deviation. The angle of deviation is usually shown with the Greek letter delta.

Key Parameters in Prism Optics:

There are some things to know about Prism Optics.

 The Angle of Incidence:(i) is the angle that the incoming ray makes with the normal of the face of the prism.

 The Angle of Emergence(e): is the angle that the outgoing ray makes with the normal of the face of the prism.

Angle of the Prism (A): The angle between the two refracting surfaces of the prism.

Refractive Index (μ): The ratio of the speed of light in a vacuum to its speed in the prism material.

Angle of Deviation in Prism Formula and Derivation

The angle of deviation in prism derivation is really important when we are talking about ray optics. We use the laws of refraction and the geometry of triangles to figure out how the external angles of the prism are related to the geometry of the prism. This is a thing we need to understand about prism derivation and it helps us learn more, about the prism itself.

The Mathematical Derivation

Consider a prism ABC where A is the angle of the prism. Let a ray of light be incident on face AB at an angle i. It refracts at an angle r1. It then hits face AC at an internal angle r2 and emerges at an angle e.

1. When we look at the shape made by the normals and the faces of the prism we can see that A = r1 + r2

2. The total deviation (δ) is the sum of deviations at each of the two surfaces: δ = (i - r1) + (e - r2)

3. Rearranging the formula gives us the primary angle of deviation in prism formula: δ = i + e - A

The Condition for Minimum Deviation

The angle of deviation gets as small as it can. This is called the angle of deviation. When the angle of deviation is, at its lowest it is called the angle of deviation. At this point:

• The angle at which something hits a surface is the same as the angle at which it leaves the surface(i = e).

• The internal refraction angles are equal (r1 = r2 = r).

• The light that bends inside the prism becomes parallel to the base of the prism. This is what happens to the refracted ray inside the prism it becomes parallel, to the base of the prism.

Using these conditions, the refractive index (μ) of the prism material can be calculated using the Prism Formula: μ = sin[(A + δm) / 2] / sin(A / 2)

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Factors on Which the Angle of Deviation in Prism Depends

The angle of deviation in a prism is something that depends on a lot of things. It depends on things and optical things. You really need to understand these things if you want to use prisms in things like spectroscopy and lens design. The angle of deviation in a prism is very important, for people who work with spectroscopy and lens design.

• The Angle of Incidence (i):The Angle of Incidence is important. When the Angle of Incidence gets bigger the Angle of Deviation gets smaller at first. It keeps getting smaller until it reaches its value, which is called the minimum Angle of Deviation. After that the Angle of Deviation starts to get bigger. The Angle of Incidence and the Angle of Deviation are related in this way.

• The Angle of the Prism (A):The Angle of the Prism is very important. If The Angle of the Prism is large it usually means that The Angle of the Prism will make the light bend more. So The Angle of the Prism really affects how much the light bends.

• The Material of the Prism: The material that a prism is made of is really important. This is because the amount of deviation that happens is directly related to something called the index. The refractive index is like a measure of how a material can bend light. If a material has a refractive index, like flint glass it will bend light a lot more than a material with a lower refractive index, like crown glass. The Material of the Prism is what determines this. For example flint glass has a refractive index, than crown glass so it bends light more.

• Wavelength of Light: The refractive index of a material varies with the wavelength of light. Shorter wavelengths (violet) deviate more than longer wavelengths (red). This is why a prism can disperse white light into a spectrum.

Practical Applications and Observations

The study of deviation is the basis for several optical instruments:

• Spectrometers: Used to measure the refractive index of glass and analyze chemical compositions.

• Periscopes and Binoculars: Utilizing total internal reflection and deviation to redirect light.

• Correction of Vision: Prisms are used in specialized eyewear to correct double vision by deviating light to land correctly on the retina.

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FAQs on Angle of Deviation in Prism

1. What is the angle of deviation in a prism?

Ans. When light goes through a prism, the angle of deviation is the angle between the extended incident ray and the emergent ray. It tells you how much the light has changed direction overall.

2. How does the angle of deviation change with the angle of incidence?

Ans. At first, the angle of deviation goes down as the angle of incidence goes up. It hits a certain low point (minimum deviation) and then starts to go up as the angle of incidence keeps becoming bigger.

3. Why does light bend toward the base?

Because of the triangular geometry; light bends toward the normal when entering and away from the normal when exiting, both of which push the ray toward the prism's thicker bottom.

4. What is the formula for the angle of deviation?

Ans.The angle of incidence is i, the angle of emergence is e, and the angle of the prism is A. The standard formula is δ = i + e - A.

5. Where can I find the best study material for  Ray Optics?

Ans. The IIT JEE Books at the PW Store have in-depth explanations of the angle of deviation and other important physics topics, so they are great for getting ready for the test.