Question

In Young's double slit experiment the two slits are illuminated by light of wavelength 5890Å and the distance between the fringes obtained on the screen is 0.2 cm. If the whole apparatus is immersed in water then the angular fringe width will be \( \dfrac{4}{3} \). The refractive index of water is:

• A. 0.30°
• B. 0.15°
• C. 15°
• D. 30°

Hint:

The fringe width in Young’s experiment is proportional to the wavelength of the light and the refractive index of the medium.

Answer 1

The Correct Option is C

Step 1: The fringe width \( \beta \) in Young's double slit experiment is given by the equation: \[ \beta = \dfrac{\lambda D}{d}, \] where \( \lambda \) is the wavelength, \( D \) is the distance between the slits and screen, and \( d \) is the separation between the slits.
Step 2: When the apparatus is immersed in water, the wavelength of the light decreases by the refractive index of water. The angular fringe width will change accordingly, and using the refractive index \( n = \dfrac{4}{3} \), the new fringe width is 15°.

Final Answer: \[ \boxed{15^\circ} \]