Question

In YDSE, second minimum is observed exactly in front of one slit. The wavelength of light used is

• A. $d^{2}/4D$
• B. $d^{2}/D$
• C. $d^2/3D$
• D. $d^2/2D$

Hint:

"Exactly in front of a slit" means $y = d/2$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
A specific fringe (2nd minimum) is located at a geometric position (in front of a slit).

Step 2: Key Formula or Approach:
1. Position of \( n \)-th minimum: \( y_n = (2n - 1) \frac{\lambda D}{2d} \).
2. Distance "in front of a slit": \( y = d/2 \).

Step 3: Detailed Explanation:
For the second minimum, \( n = 2 \).
\[ y_2 = (2 \times 2 - 1) \frac{\lambda D}{2d} = \frac{3\lambda D}{2d} \]
Given this is in front of one slit:
\[ \frac{3\lambda D}{2d} = \frac{d}{2} \]
\[ 3\lambda D = d^2 \]
\[ \lambda = \frac{d^2}{3D} \]

Step 4: Final Answer:
The wavelength is \( \frac{d^2}{3D} \).