Question

In the diffraction pattern due to a single slit of width '\(a\)' with incident light of wavelength '\(\lambda\)', at an angle of diffraction '\(\theta\)', the condition for the second maximum is

• A. \(a\sin \theta =2\lambda\)
• B. \(2\lambda \sin \theta =3a\)
• C. \(5\lambda \sin \theta =3a\)
• D. \(2a\sin \theta =5\lambda\)

Hint:

Secondary maxima in single slit diffraction occur when the path difference is an odd multiple of half the wavelength.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a single slit of width \(a\), the secondary maxima occur at \(a\sin\theta = \dfrac{(2n+1)\lambda}{2}\), where \(n = 1, 2, 3, \ldots\)

Step 2: Second Maximum
The second secondary maximum corresponds to \(n = 2\).

Step 3: Substitute
\(a\sin\theta = \dfrac{5\lambda}{2}\)

Step 4: Rearrange
\(2a\sin\theta = 5\lambda\)

Final Answer:
The condition for the second maximum is \(2a\sin\theta = 5\lambda\). \[ \boxed{\text{(D) }2a\sin\theta=5\lambda} \]