Question 63: Wave Optics

Question

Which of the following are true for a single slit diffraction?
A. Width of central maxima increases with increase in wavelength keeping slit width constant.
B. Width of central maxima increases with decrease in wavelength keeping slit width constant.
C. Width of central maxima increases with decrease in slit width at constant wavelength.
D. Width of central maxima increases with increase in slit width at constant wavelength.
E. Brightness of central maxima increases for decrease in wavelength at constant slit width.

Accepted Answer

In a single slit diffraction experiment the linear width $(W)$ of the central maximum on a screen at distance $D$ is given by the formula:
$$ \mathrm{W}=\frac{2 \lambda \mathrm{D}}{\mathrm{a}} $$
Where :
1. $\lambda$ is the wavelength of the light.
2. a is the width of the slit.
From the formula, the width of the central maximum is directly proportional to the wavelength ( $\mathrm{W} \propto \lambda$ ) when the slit width (a) is kept constant.
This means if the wavelength increases, the width of the central maximum also increases. Therefore, Statement A is true and Statement B is false.
From the formula, the width of the central maximum is inversely proportional to the slit width ( $\mathrm{W} \propto \frac{1}{\mathrm{a}}$ ) when the wavelength ( $\lambda$ ) is kept constant.
This means if the slit width decreases, the width of the central maximum increases. Therefore, Statement C is true and Statement D is false.
The peak intensity (brightness) of the central maximum depends on how the superposition of waves on screen occurs. For a given incident intensity, the power passing through the slit is constant for a fixed slit width. When the wavelength decreases, the central maximum becomes narrower (the angular width decreases). Because the exact same amount of energy is now concentrated into a smaller area, the peak brightness of the central maximum increases. Therefore, Statement E is true.
Hence, the true statements are $\mathbf{A}, \mathbf{C}$, and $\mathbf{E}$.

Answer

B, D only

Answer

A, D only

Answer

A, C, E only

Answer

B, C only

Wave Optics

Choose the correct answer: