Question

The direction of the second order diffraction minima in Fraunhofer diffraction at a single slit (\(a=\) slit width) is given by

• A. \(\sin\theta=\dfrac{\lambda}{2a}\)
• B. \(\sin\theta=\dfrac{2\lambda}{a}\)
• C. \(\sin\theta=2\lambda a\)
• D. \(\sin\theta=\dfrac{a}{2\lambda}\) \bigskip

Hint:

For single-slit Fraunhofer diffraction, \[ a\sin\theta=n\lambda \] gives the positions of minima. \[ n=1 \Rightarrow \text{First minimum}, \qquad n=2 \Rightarrow \text{Second minimum}, \qquad n=3 \Rightarrow \text{Third minimum}. \]

Answer 1

The Correct Option is B

Concept: For single-slit diffraction minima: \(a\sin\theta = n\lambda\). For second minimum, \(n=2\).

Step 1: \(a\sin\theta = 2\lambda \Rightarrow \sin\theta = 2\lambda/a\).

Step 2: Write the final answer. \(\boxed{\sin\theta=\frac{2\lambda}{a}}\)