
Write the formula to get the refractive index of the prism and write the terms in it.
Answer
489.3k+ views
Hint Draw a ray diagram showing the refraction inside and outside a prism. Use exterior angle property, angle sum property of a triangle and a quadrilateral and hence find a relation between incident angle, angle of deviation, and prism angle. Consider the ray of light to undergo a minimum angle of deviation and approximate the incident angle and emergent angle. Finally, substitute the derived value of incident and refracted angle into Snell’s law.
Complete step by step answer:
Let us consider a prism with a refractive index . Let and be normal lines to the faces and respectively. Let the incident angle on the face be and the refracted angle on this face be . Let the incident angle on the face be and the refracted ray after passing through be . We will extend the ray lines- and to the point . Let the angle of deviation be .
In the quadrilateral , the sum of all four angles must be .
But here, as they are normal rays.
Rearranging the above equation gives us
is an exterior angle in the triangle, .
Therefore, using the exterior angle property for the triangle gives us .
From the figure, let and
By using the exterior angle property for the triangle ,
By substituting as and as , we get
But we have already proved that ,
In the case of minimum deviation, and .
Substituting these values in the above equation, we get
Now let us write Snell’s law for the prism,
From the already calculated values of and , we get
This is the equation of the refractive index for a prism with the prism angle - and angle of minimum deviation - .
Note
A minimum angle of deviation in a prism means that the incident and the emergent angles will be equal, the refracted angles inside will be equal and the refracted ray will run parallel to the base of the prism. We use Snell’s law as the medium is getting changed.
Complete step by step answer:

Let us consider a prism
In the quadrilateral
But here,
Rearranging the above equation gives us
Therefore, using the exterior angle property for the triangle
From the figure, let
By using the exterior angle property for the triangle
By substituting
But we have already proved that
In the case of minimum deviation,
Substituting these values in the above equation, we get
Now let us write Snell’s law for the prism,
From the already calculated values of
This is the equation of the refractive index for a prism with the prism angle -
Note
A minimum angle of deviation in a prism means that the incident and the emergent angles will be equal, the refracted angles inside will be equal and the refracted ray will run parallel to the base of the prism. We use Snell’s law as the medium is getting changed.
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Which one of the following is a true fish A Jellyfish class 12 biology CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Write the difference between solid liquid and gas class 12 chemistry CBSE
