Question

For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _____.

• A. \(3:4\)
• B. \(3:2\)
• C. \(2:1\)
• D. \(1:2\)

Answer 1

The Correct Option is B

Concept: For a prism at minimum deviation: \[ \mu = \frac{\sin\left(\frac{A+\delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \] For a thin symmetric prism \(A\) is small and the approximate relation holds: \[ \delta_m = (\mu-1)A \] Also at minimum deviation condition: \[ i = \frac{A+\delta_m}{2} \]
Step 1:Substitute the deviation relation} \[ i = \frac{A + (\mu-1)A}{2} \] \[ i = \frac{\mu A}{2} \]
Step 2:Compute the ratio} \[ \frac{i}{\delta_m} = \frac{\frac{\mu A}{2}}{(\mu-1)A} \] \[ = \frac{\mu}{2(\mu-1)} \] Substitute \(\mu = 1.5\): \[ \frac{i}{\delta_m} = \frac{1.5}{2(0.5)} \] \[ = \frac{1.5}{1} \] \[ = \frac{3}{2} \] Thus \[ i : \delta_m = 3 : 2 \] \[ \boxed{3:2} \]