Question

The refractive index of a transparent liquid filled in an equilateral hollow prism is √2. The angle of minimum deviation for the liquid will be____.

Answer 1

Correct Answer: 30

To determine the angle of minimum deviation (D) for the transparent liquid, we first need to understand the relationship between the refractive index (n), the prism angle (A), and the angle of minimum deviation. For an equilateral prism, the prism angle (A) is 60°.

The formula relating these variables is given by:
n = (sin((A+D)/2))/(sin(A/2))

Given: n = √2, A = 60°.

We substitute the given values into the formula:
√2 = (sin((60°+D)/2))/(sin(60°/2))

Calculating sin(30°):
sin(30°) = 0.5

Substituting back into the equation:
√2 = sin((60°+D)/2) / 0.5

Thus:
sin((60°+D)/2) = √2 * 0.5 = √2/2

Recognizing that sin(45°) = √2/2, we equate the angles:
(60°+D)/2 = 45°

Solving for D:
60° + D = 90°
D = 90° - 60°
D = 30°

The angle of minimum deviation is thus 30°, fitting perfectly within the given range of 30 to 30.