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A ray of light is incident on a 60^(@) p...

A ray of light is incident on a `60^(@)` prism at the minimum deviation position. The angle of refraction at the first face (i.e. incident face) of the prism is-

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

Zero

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the angle of refraction at the first face of a prism when light is incident at the minimum deviation position. Here's the step-by-step solution: ### Step 1: Understand the Prism and Minimum Deviation We are given a prism with an angle \( A = 60^\circ \). At the minimum deviation position, the light ray experiences equal angles of refraction at both faces of the prism. ### Step 2: Use the Relation for Minimum Deviation At minimum deviation, the angles of refraction \( r_1 \) and \( r_2 \) at the two faces of the prism are equal. Therefore, we can denote both angles as \( r \). ### Step 3: Apply the Formula for Prism The relation for the angles in a prism at minimum deviation is given by: \[ A = r_1 + r_2 \] Since \( r_1 = r_2 = r \), we can rewrite this as: \[ A = 2r \] ### Step 4: Substitute the Given Angle Substituting the value of the angle of the prism \( A \): \[ 60^\circ = 2r \] ### Step 5: Solve for \( r \) Now, we can solve for \( r \): \[ r = \frac{60^\circ}{2} = 30^\circ \] ### Conclusion Thus, the angle of refraction at the first face of the prism is \( 30^\circ \). ### Final Answer The angle of refraction at the first face of the prism is \( 30^\circ \). ---
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