Question

In YDSE, \( \lambda = 600\ \text{nm} \), fifth fringe at 6 mm. When \( \lambda = 400\ \text{nm} \), third fringe is at:

• A. 1.6 mm
• B. 2 mm
• C. 2.4 mm
• D. 3 mm

Hint:

Fringe width is directly proportional to both order and wavelength: \( x \propto n\lambda \)

Answer 1

The Correct Option is C

Fringe position \( x = n\lambda D/d \Rightarrow x \propto n \lambda \) Given: \[ x_1 = 6\ \text{mm}, n_1 = 5,\ \lambda_1 = 600\ \text{nm} \Rightarrow \frac{x_2}{x_1} = \frac{n_2 \lambda_2}{n_1 \lambda_1} = \frac{3 \cdot 400}{5 \cdot 600} = \frac{1200}{3000} = \frac{2}{5} \Rightarrow x_2 = \frac{2}{5} \cdot 6 = 2.4\ \text{mm} \]