Question

Find the angle $A$ of the second prism so that the light ray suffers dispersion without deviation: 

• A. $6^\circ$
• B. $4^\circ$
• C. $7^\circ$
• D. $2^\circ$

Hint:

For combinations of thin prisms, use $\delta = (\mu - 1)A$. Equal and opposite deviations ensure no net deviation, while different refractive indices cause dispersion.

Answer 1

The Correct Option is B

Concept: For a prism of small angle, the deviation produced is given by: \[ \delta = (\mu - 1)A \] For dispersion without deviation, the net deviation produced by the combination of prisms must be zero, while refractive indices are different for different colors.
Step 1: From the diagram, the first prism has: \[ A_1 = 5^\circ, \quad \mu_1 = 1.72 \] The second prism has: \[ A_2 = A, \quad \mu_2 = 1.90 \]
Step 2: For no net deviation: \[ (\mu_1 - 1)A_1 = (\mu_2 - 1)A_2 \]
Step 3: Substitute the given values: \[ (1.72 - 1)\times 5 = (1.90 - 1)\times A \] \[ 0.72 \times 5 = 0.90 \times A \] \[ A = \frac{3.6}{0.9} = 4^\circ \] Step 4: Thus, the required angle of the second prism is: \[ \boxed{4^\circ} \]