Question

In Young's double slit experiment, the angular width of a fringe is found to be \(0.2^{\circ}\) on a screen placed 1m away. The wavelength of light used in 600 nm. If the entire apparatus is immersed in water of refractive index 4/3. the angular width of the fringe will be

• A. \(0.10^{\circ}\)
• B. \(0.15^{\circ}\)
• C. \(0.20^{\circ}\)
• D. \(0.25^{\circ}\)

Hint:

The wavelength in water is the air wavelength divided by the refractive index, and angular width is proportional to wavelength.

Answer 1

The Correct Option is B

Step 1: Use the speed of light.
In water the speed is $c/\mu$ and the frequency is unchanged, so $\lambda_w = \lambda/\mu = 600\times\dfrac{3}{4} = 450$ nm.

Step 2: Ratio.
$\dfrac{\theta_w}{\theta_a} = \dfrac{450}{600} = 0.75$.

Step 3: Result.
$\theta_w = 0.75\times0.2^\circ = 0.15^\circ$.

Final Answer:
Option (B). \[ \boxed{0.15^\circ} \]