Question

A monochromatic light of wavelength \( 6000 \, \mathring{A} \) is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in A is \( \frac{1}{2} \) that of B. If the refractive index of A is \( \frac{4}{3} \), find the refractive index of B.

• A. \( \frac{4}{3} \)
• B. \( \frac{3}{5} \)
• C. \( \frac{3}{2} \)
• D. \( \frac{5}{3} \)

Hint:

Number of waves depends on refractive index and thickness of medium.

Answer 1

The Correct Option is D

Step 1: Relation for number of waves.
\[ n = \frac{\text{path}}{\lambda'} \]

Step 2: Wavelength in medium.
\[ \lambda' = \frac{\lambda}{\mu} \]

Step 3: Number of waves expression.
\[ n = \frac{\mu \cdot t}{\lambda} \]

Step 4: Apply given condition.
\[ n_A = \frac{1}{2} n_B \]

Step 5: Substitute.
\[ \frac{\mu_A t_A}{\lambda} = \frac{1}{2} \cdot \frac{\mu_B t_B}{\lambda} \]

Step 6: Simplify.
\[ \mu_A t_A = \frac{1}{2} \mu_B t_B \]
\[ \frac{4}{3} \cdot 10 = \frac{1}{2} \mu_B \cdot 16 \]
\[ \frac{40}{3} = 8\mu_B \Rightarrow \mu_B = \frac{5}{3} \]

Step 7: Final Answer.
\[ \boxed{\frac{5}{3}} \]