Question

A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between the 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit is:

• A. \( \dfrac{3D\lambda}{a} \)
• B. \( \dfrac{3D\lambda}{2a} \)
• C. \( \dfrac{D\lambda}{a} \)
• D. \( \dfrac{2D\lambda}{a} \)

Answer 1

The Correct Option is D

Concept:
For single slit diffraction, the position of minima on the screen is \[ y_n=\frac{nD\lambda}{a}, \qquad n=1,2,3,... \] Step 1: Position of the first minima. \[ y_1=\frac{D\lambda}{a} \] Step 2: Position of the third minima. \[ y_3=\frac{3D\lambda}{a} \] Step 3: Find the separation. \[ \text{Separation}=y_3-y_1 \] \[ =\frac{3D\lambda}{a}-\frac{D\lambda}{a} \] \[ =\frac{2D\lambda}{a} \]