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: Concept
Position of slits is $y = d/2$.

Step 2: Analysis
Condition for $m^{th}$ minimum: $y = (2m-1)\frac{\lambda D}{2d}$.
For second minimum ($m=2$): $y = \frac{3\lambda D}{2d}$.

Step 3: Calculation
$\frac{d}{2} = \frac{3\lambda D}{2d} \implies d^2 = 3\lambda D \implies \lambda = \frac{d^2}{3D}$.

Step 4: Conclusion
Hence, $\lambda = d^{2}/3D$. Final Answer: (C)