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.

In single slit diffraction, the angular half-width of the central maximum is given by $$\sin\theta = \frac{\lambda}{a}$$, where $$\lambda$$ is the wavelength and $$a$$ is the slit width. For small angles, the linear width of the central maximum on a screen at distance $$D$$ is $$W = \frac{2\lambda D}{a}$$.

Statement A: Width increases with increase in wavelength (constant slit width). Since $$W \propto \lambda$$, increasing $$\lambda$$ increases $$W$$. Statement A is TRUE.

Statement B: Width increases with decrease in wavelength. This contradicts $$W \propto \lambda$$. Statement B is FALSE.

Statement C: Width increases with decrease in slit width (constant $$\lambda$$). Since $$W \propto \frac{1}{a}$$, decreasing $$a$$ increases $$W$$. Statement C is TRUE.

Statement D: Width increases with increase in slit width. Since $$W \propto \frac{1}{a}$$, increasing $$a$$ decreases $$W$$. Statement D is FALSE.

Statement E: Brightness of central maximum increases for decrease in wavelength (constant slit width). The total light energy passing through the slit is fixed, but when $$\lambda$$ decreases, the central maximum becomes narrower ($$W \propto \lambda$$), so the same energy is concentrated into a smaller area. Since intensity = energy per unit area, the peak brightness increases when $$\lambda$$ decreases. Statement E is TRUE.

The true statements are A, C, and E. The answer is Option A.