Question

The fringe width for red colour as compare to that for violet colour is approximately

• A. 4 times
• B. 3 times
• C. 8 times
• D. double

Answer 1

The Correct Option is D

Fringe Width in Double-Slit Interference

The fringe width in a double-slit interference pattern is given by the formula:

\[ w = \frac{\lambda L}{d} \]

Here, the wavelength \(\lambda\) is directly proportional to the fringe width \(w\).

- Red light has a wavelength of approximately 700 nm.
- Violet light has a wavelength of approximately 400 nm.

To compare the fringe widths:

\[ \frac{w_r}{w_v} = \frac{\lambda_r}{\lambda_v} \]

Substituting values:

\[ \frac{w_r}{w_v} \approx \frac{700}{400} \approx 1.75 \]

This means the fringe width for red light is about 1.75 times that of violet light.

Since none of the given answer choices (A, B, C, D) match this exactly, the closest option is (D) "double", suggesting that the fringe width of red light is nearly twice that of violet light.