Physics - Wave Optics Question with Solution | TestHub

In a single slit diffraction pattern, the condition for the first minimum is given by $a\sin \theta =\lambda$, where $a$ is the slit width, $\lambda$ is the wavelength, and $\theta$ is the angular position of the first minimum.

For small angles, $\sin \theta \approx \theta$, so $\theta =\frac{\lambda }{a}$.

The angular width of the central maximum is the angle between the first minima on either side of the center, which is $2\theta =\frac{2\lambda }{a}$.

The linear width of the central maximum on a screen at a distance $D$ from the slit is given by $W=D(2\theta )$.

Substituting the value of $2\theta$, we get $W=\frac{2D\lambda }{a}$.

Answer: $2D\lambda /a$