Question

The thin prism having refracting angle \(10^{\circ }\) is made of glass of refractive index \(1.42\). This prism is combined with another thin prism of glass of refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism is

• A. \(4^{\circ }\)
• B. \(6^{\circ }\)
• C. \(8^{\circ }\)
• D. \(10^{\circ }\)

Hint:

For no deviation the two thin prisms deviate by equal amounts in opposite senses.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
A thin prism deviates light by \(\delta=(\mu-1)A\). For dispersion without deviation the prisms are placed opposite ways so the deviations cancel.

Step 2: Condition
\((\mu_1-1)A_1=(\mu_2-1)A_2\).

Step 3: Calculation
\((1.42-1)\times10=(1.7-1)A_2\), so \(4.2=0.7A_2\).

Step 4: Result
\(A_2=6^{\circ}\).

Final Answer:
The refracting angle of the second prism is 6 degrees. \[ \boxed{\text{(B) }6^{\circ}} \]