Question

If Young's double slit experiment is performed in water

• A. the fringe width will decrease
• B. the fringe width will increase
• C. the fringe width will remain unchanged
• D. the fringe width first decreases and then increases

Hint:

Fringe width is proportional to the wavelength, and the wavelength of light is smaller in a medium of higher refractive index.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The fringe width is \(\beta = \dfrac{\lambda D}{d}\).
It depends directly on the wavelength of light.

Step 2: Effect of Water
In water of refractive index \(\mu\), the wavelength becomes \(\lambda' = \dfrac{\lambda}{\mu}\).

Step 3: New Fringe Width
\(\beta' = \dfrac{\lambda' D}{d} = \dfrac{\beta}{\mu}\)

Step 4: Conclusion
Since \(\mu > 1\) for water, \(\beta' < \beta\), so the fringe width decreases.

Final Answer:
The fringe width decreases when the experiment is done in water. \[ \boxed{\text{(A) }\text{the fringe width will decrease}} \]