Question

A glass slab of thickness \(4\,\text{cm}\) contains the same number of waves as in \(x\,\text{cm}\) of water column when both are traversed by the same monochromatic light. If the refractive indices of glass and water for that light are \( \frac{5}{3} \) and \( \frac{4}{3} \) respectively, the value of \(x\) will be

• A. \( \frac{9}{20}\,\text{cm} \)
• B. \( \frac{5}{4}\,\text{cm} \)
• C. \( 5\,\text{cm} \)
• D. \( \frac{20}{9}\,\text{cm} \)

Hint:

Number of waves depends on optical path length \( (\mu t) \), not on wavelength alone.

Answer 1

The Correct Option is C

Step 1: Use relation for number of waves.
\[ \text{Number of waves} = \frac{\mu t}{\lambda_0} \]

Step 2: Apply equality condition.
\[ \frac{\mu_g t_g}{\lambda_0} = \frac{\mu_w x}{\lambda_0} \]

Step 3: Substitute values.
\[ \frac{5}{3} \times 4 = \frac{4}{3} \times x \] \[ x = 5\,\text{cm} \]