Question

If we observe the single slit Fraunhofer diffraction with wavelength $\lambda$ and slit width $b$, the angular width $\left({\theta }_w\right)$ of the central maxima is $2\theta$. On decreasing the slit width for the same $\lambda$

• A. $\theta$ increases
• B. $\theta$ remains inchanged
• C. $\theta$ decreases
• D. $\theta$ increases or decreases depending on the intensity of light

Answer 1

The correct option is A $\theta$ increases

Angular width of central maxima when a light wave of wavelength $\lambda$ is diffracted by a single slit of width $b$ is given by

${\theta }_w=\frac{2\lambda }{b}$

According to the question,
${\theta }_w=2\theta$

$\Rightarrow 2\theta =\frac{2\lambda }{b}$

$\Rightarrow \theta =\frac{\lambda }{b}$

$\therefore$ When $b$ decreases, $\theta$ increases.

Hence, the correct option is $\left(A\right)$

Why this question? Concept: To understand the effect of slit width on the width of dark and bright fringes.