Question

In a Fraunhoffer diffraction, light of wavelength '\(\lambda\)' is incident on slit of width ' d '. The diffraction pattern is observed on a screen placed at a distance ' D '. The linear width of central maximum is equal to two times the width of the slit, then 'D' has value

• A. \(\frac{d^2}{\lambda}\)
• B. \(\frac{d^2}{2\lambda}\)
• C. \(\frac{d^2}{3\lambda}\)
• D. \(\frac{d^2}{4\lambda}\)

Hint:

Central maximum width = \(2\lambda D/d\)

Answer 1

The Correct Option is A

Concept:
Width of central maximum: \[ \beta = \frac{2\lambda D}{d} \] Step 1: Given condition. \[ \beta = 2d \]
Step 2: Substitute. \[ \frac{2\lambda D}{d} = 2d \]
Step 3: Solve. \[ \lambda D = d^2 \Rightarrow D = \frac{d^2}{\lambda} \]
Step 4: Conclusion. \[ D = \frac{d^2}{\lambda} \]