Angle of Deviation

Angle of deviation is a term belongs to the topic refraction of a light through a prism which states that when a light ray incident on a prism, after passing through the prism it gets refracted due to change in medium and after refraction it strikes on the second surface of a prism and it emerges out as an emergent ray. But in the absence of a prism the incident ray would move straight without any refraction.  Due to refraction it gets deviated by some angle which is known as angle of deviation and it is denoted by delta  .

Some important notations used in refraction:

∠i-angle of incidence

∠e-angle of emergence

∠δ-angle of deviation

∠A-angle of prism

To get the thorough knowledge of angle of deviation it’s really important to have a basic knowledge about its related terms such as:

• Incident ray – the light ray which travels from a light source incident or (strike) on an object is known as incident ray.

• Refracted ray – the ray which gets refracted or bent towards or away from normal due to change in media is known as refracted ray.

• Normal- the perpendicular line drawn between incident ray and refracted ray.

• Emergent ray – in a prism, after refraction the refracted ray passes through the other side of a prism and is known as refracted ray.

• Angle of incidence – it is the angle formed between incident ray and normal.

• Angle of deviation – the angle between the incident ray and the emergent ray is known as angle of deviation.

• Angle of emergence – emergent ray makes an angle with normal known as angle of emergence.

• Refraction – a phenomenon of bending of a light ray when it passes from one medium to another medium due to difference in optical densities of medium is known as refraction of light. 

Refraction through a prism

Let us consider a ray PQ strikes on a surface of prism AB. As it enters from rarer medium to denser medium (air to glass), it will bend towards normal along a path QR. This QR is known as refracted ray. When this refracted ray strikes on another surface say AC of a prism it will bend away from normal as now, it emerges from denser to rarer medium and it is known as emergent ray. The angle between the incident ray and the emergent ray is known as angle of deviation and it is denoted by delta δ. 

Derivation of refraction through a prism 

Let us consider a prism ABC,

In which PQ is incident ray 

QR IS refracted ray 

RS is emergent ray 

A – angle of prism 

AQNR is a quadrilateral, two angles (at the vertex Q and R) are right angles. 

Therefore, the sum of other angles of  a quadrilateral is 180°

∠A+ ∠QNR=180° …..1

From right angle triangle QNR 

r1 + r2  + ∠QNR=180° …..2

r1 , r2 – angle of refraction at face 1 and 2 of a prism.

On Comparing equation 1 and 2

r1 + r2 = A 

the total deviation is the sum of deviations at the two face

δ=i-r1+(e-r2)

δ=i+e-A

Thus, we can say that angle of deviation depends upon angle of incidence.

Factors on which angle of deviation depends 

1. The angle of incidence 

2. The wavelength of light used 

3. The material of the prism 

4. The angle of prism 

Angle of minimum deviation: the minimum value of angle of deviation suffered by a ray on passing through a prism is known as angle of minimum deviation m. 

The Relationship – refractive index and angle of minimum deviation 

 i = i’, r=r’ , δ=δm 

as, A+ δ=i+i’

∴A+ δm = i+i’ or i=A+m / 2 

A = r + r’ = r+ r = 2r 

∵ r= A/2

From Snell’s law, the refractive index of a prism 

μ=sinisinr or μ=sin A+m2sinA/2  

Deviation through a prism of small angle 

Suppose a light is incident at a small angle i on the prism then angles r,r’, and i’ will also be small

For refraction at face AB 

μ=sinisinr=ir   →i= μr

For refraction at face AC

μ=sini’sinr’=i’r’  →i=μr’

Hence, angle of deviation produced by the prism is

δ=i+i’-A= μr’-A

=μr+r’-A=μA-A

δ=μ-1A

∵r+r’=A

Refractive index (μ)

Refractive index of a medium for a light of given wavelength is defined as the ratio of speed of light in vacuum to its speed in that medium.

Refractive index = speed of light in vacuum / speed of light in medium 

It is represented by µ.

 The formula of refractive index is:

 µ = c/v 

where, c- speed of light 

v- phase velocity of light

Factors on which refractive index of a medium depends 

• Nature of medium 

• Wavelength of the light used 

• Nature of the surrounding medium 

• temperature

Conclusion 

In this article we have learned about angle of deviation: the angle between the incident ray and the emergent ray is known as angle of deviation. It is denoted by delta δ. Refraction through a prism δ=i+e- A.   Factors on which angle of deviation depends: angle of incidence, The wavelength of light used, the material of the prism, the angle of prism. The relationship between refractive index and angle of minimum deviation is given by: μ=sinisinr or μ=sin A+m2sinA/2 . Factors on which refractive index of a medium depends: Nature of medium, Wavelength of the light used, Nature of the surrounding medium ,temperature.