
Write the formula of the angle of minimum deviation produced by a thin prism.
Answer
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Hint: Start by using the equation of prism . Since the angles are small and the equation now becomes . Then use the snell’s law and since angles are small , , and . Use these values to obtain the equation and . Then use simple geometry to obtain the equation . Then put the value in the previous equation to reach the solution.
Complete answer:
The angle of deviation is the angle that the emerging ray coming out of a prism makes with the incident ray coming in the prism (indicated as angle D in the diagram below). This angle of deviation decreases with an increase in the angle of incidence, but only up to a minimum angle called the angle of minimum deviation (indicated by ).
The refractive index of the material of the prism is calculated by using the following formula
(Equation 1)
The refractive index of the material of the prism
The angle of the prism
Angle of deviation
For thin prisms or small angle prisms, as the angles become very small, the sine of the angle nearly equals the angle itself, i.e. and .
Putting these values in equation 1, we get
Now, for the angle of minimum deviation this equation becomes
We know by Snell’s law for the incident ray
Since the angles are small, so and .
So,
We know by Snell’s law for the emergent ray
Since the angles are small, so and .
So,
We know,
(Vertically opposite Angles)
(Vertically opposite angles)
In ,
( is an external angle to the triangle )
(Equation 1)
In the sum of all the angles is
Substituting this value in equation 1, we get
For, the angle of minimum deviation, , so equation 2 becomes
Note:
The prism is optical equipment that is used to observe the dispersion of white light. The prism makes use of the fact that light travels with different speeds in different mediums. The prism is normally made out of glass, the edges of the prism should be perfect during the manufacturing of the glass prisms.
Complete answer:
The angle of deviation is the angle that the emerging ray coming out of a prism makes with the incident ray coming in the prism (indicated as angle D in the diagram below). This angle of deviation decreases with an increase in the angle of incidence, but only up to a minimum angle called the angle of minimum deviation (indicated by

The refractive index of the material of the prism is calculated by using the following formula
For thin prisms or small angle prisms, as the angles become very small, the sine of the angle nearly equals the angle itself, i.e.
Putting these values in equation 1, we get
Now, for the angle of minimum deviation this equation becomes
We know by Snell’s law for the incident ray
Since the angles are small, so
So,
We know by Snell’s law for the emergent ray
Since the angles are small, so
So,
We know,
In
In
Substituting this value in equation 1, we get
For, the angle of minimum deviation,
Note:
The prism is optical equipment that is used to observe the dispersion of white light. The prism makes use of the fact that light travels with different speeds in different mediums. The prism is normally made out of glass, the edges of the prism should be perfect during the manufacturing of the glass prisms.
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