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If the refracting angle of a prism is 60...

If the refracting angle of a prism is `60^@` and the minimum deviation is `30^@`, then the angle of incidence is

A

(a)`30^@`

B

(b)`45^@`

C

(c)`60^@`

D

(d)`90^@`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the angle of incidence (i) when the refracting angle of the prism (A) is given as \(60^\circ\) and the minimum deviation (\(\delta_m\)) is given as \(30^\circ\). ### Step-by-Step Solution: 1. **Identify the given values**: - Refracting angle of the prism, \(A = 60^\circ\) - Minimum deviation, \(\delta_m = 30^\circ\) 2. **Use the formula for angle of incidence**: The formula to find the angle of incidence (i) in terms of the angle of the prism and the minimum deviation is: \[ i = \frac{A + \delta_m}{2} \] 3. **Substitute the known values into the formula**: \[ i = \frac{60^\circ + 30^\circ}{2} \] 4. **Calculate the sum in the numerator**: \[ 60^\circ + 30^\circ = 90^\circ \] 5. **Divide by 2 to find the angle of incidence**: \[ i = \frac{90^\circ}{2} = 45^\circ \] 6. **Conclusion**: The angle of incidence is \(45^\circ\). ### Final Answer: The angle of incidence is \(45^\circ\). ---
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