Calculate the angle of minimum deviation of a 60º prism of a refractive index 1.5[ (sin^{-1}) (0.75) = 49º]
-
A.
38o -
B.
19.47o -
C.
16.25o -
D.
49o
Correct Answer: Option A
Explanation
For a refractive index () = (frac{sinfrac{1}{2} (A + D)}{sinfrac{1}{2}A})
D = angle of minimum deviation
A = refractive angle of the prism
1.5 = (frac{sinfrac{1}{2} (60 + D)}{sinfrac{1}{2} times 60})
1.5 = (frac{sinfrac{1}{2} (60 + D)}{sin 30})
Sin (frac{1}{2}) (60 + D) = 1.5 * Sin 30
Sin (frac{1}{2}) (60 + D) = 0.75
(frac{1}{2}) (60 + D) = Sin-1 (0.75)
but Sin-1 (0.75) = 49o
(frac{1}{2}) (60 + D) = 49
60 + D = 2 * 49 = 98o
D = 98o – 60o
D = 38o
There is an explanation video available below.