Question

A thin prism \( P \) of angle 4° made up of glass of refractive index 1.48 is combined with another prism \( Q \) made up of glass of refractive index 1.64 to produce dispersion without deviation. The angle of prism \( Q \) is

• A. 5°
• B. 3°
• C. 6°
• D. 4°

Hint:

In problems involving dispersion without deviation, the deviation produced by each prism must be equal and opposite.

Answer 1

The Correct Option is B

Step 1: Condition for dispersion without deviation.
When two prisms are combined to produce dispersion without deviation, the deviation caused by the first prism must be compensated by the second prism. This means that the deviation caused by the two prisms must be equal and opposite. The deviation \( \delta \) produced by a prism is given by: \[ \delta = (\mu - 1) \cdot A \] where \( \mu \) is the refractive index of the material and \( A \) is the angle of the prism.
Step 2: Applying the condition.
For dispersion without deviation, we have: \[ (\mu_P - 1) \cdot A_P = (\mu_Q - 1) \cdot A_Q \] Substituting the values: \[ (1.48 - 1) \cdot 4 = (1.64 - 1) \cdot A_Q \] Solving for \( A_Q \), we get: \[ A_Q = 3^\circ \] Step 3: Conclusion.
Thus, the angle of prism \( Q \) is 3°, corresponding to option (B).