Question

Angular width of central maxima increases when:

• A. \(\lambda\) increases
• B. \(\lambda\) decreases
• C. \(e\) increases
• D. \(e\) decreases

Hint:

For diffraction patterns: \[ \theta = \frac{2\lambda}{e} \] Larger wavelength or smaller slit width produces broader diffraction patterns.

Answer 1

The Correct Option is A

Concept: In single slit diffraction, the angular width of the central bright fringe is given by: \[ \theta = \frac{2\lambda}{e} \] where:

• \(\theta\) = angular width of central maxima
• \(\lambda\) = wavelength of light
• \(e\) = width of the slit

From the formula: \[ \theta \propto \lambda \] and \[ \theta \propto \frac{1}{e} \] Thus, angular width increases with increase in wavelength and decreases with increase in slit width.

Step 1: Write the formula for angular width.
For single slit diffraction: \[ \theta = \frac{2\lambda}{e} \] This formula directly relates angular width with wavelength and slit width.

Step 2: Analyze the effect of wavelength.
Since: \[ \theta \propto \lambda \] when wavelength increases, angular width also increases. Therefore: \[ \lambda \uparrow \Rightarrow \theta \uparrow \]

Step 3: Analyze the effect of slit width.
Since: \[ \theta \propto \frac{1}{e} \] when slit width increases, angular width decreases. Thus: \[ e \uparrow \Rightarrow \theta \downarrow \]

Step 4: Choose the correct option.
Among the given choices, only increase in wavelength increases angular width. Hence, the correct answer is: \[ \boxed{\lambda \text{ increases}} \]