Q.A parallel beam of light of wavelength $500\ \text{nm}$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen $1\ \text{m}$ away. It is observed that the first minimum is at a distance of $2.5\ \text{mm}$ from the centre of the screen. Find the width of the slit.

The first minimum of a single-slit diffraction pattern occurs at a definite angle set by the slit width and wavelength, so measuring where that minimum falls on the screen lets us solve directly for …

Step 1: Condition for the first minimum in single-slit diffraction

For a single slit of width $a$, the first minimum occurs at an angle $\theta$ satisfying:

Step 2: Relate the angle to the measured position on screen

For a screen at distance $D$ and the minimum observed at a distance $y$ from the centre, and since $\theta$ is small:

Step 3: Combine and solve for $a$

Step 4: Substitute the given values …