Question

A parallel beam of monochromatic light falls normally on a single narrow slit. The angular width of the central maximum in the resulting diffraction pattern

• A. decreases with increase of slit width.
• B. increases with increase of slit width.
• C. decreases with decrease of slit width.
• D. may increase or decrease.

Hint:

In diffraction, the angular width of the central maximum is inversely proportional to the slit width. A larger slit results in a narrower central maximum.

Answer 1

The Correct Option is A

Step 1: Diffraction and slit width.
In single-slit diffraction, the angular width \( \theta \) of the central maximum is given by: \[ \sin \theta = \frac{\lambda}{a} \] where \( \lambda \) is the wavelength of the light and \( a \) is the width of the slit.
Step 2: Relationship between slit width and angular width.
From the equation, it is clear that as the slit width \( a \) increases, the angular width \( \theta \) decreases. This means the central maximum becomes narrower.
Step 3: Conclusion.
The angular width of the central maximum decreases with an increase in slit width, which corresponds to option (A).