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.

• A. A, D, E only
• B. B, C only
• C. A, D only
• D. B, D only

Hint:

For single slit diffraction, remember: width of central maximum is directly proportional to wavelength and inversely proportional to slit width.

Answer 1

The Correct Option is C

In single slit diffraction, the angular width of the central maximum is given by: \[ \theta = \frac{2\lambda}{a} \] where $\lambda$ is the wavelength of light and $a$ is the slit width.

Step 1: Analyze statement A.
If slit width $a$ is constant and wavelength $\lambda$ increases, then: \[ \theta \propto \lambda \] Hence, width of the central maximum increases.
Statement A is correct.

Step 2: Analyze statement B.
If wavelength decreases while slit width is constant, the angular width decreases.
Statement B is incorrect.

Step 3: Analyze statement C.
If slit width $a$ decreases at constant wavelength: \[ \theta \propto \frac{1}{a} \] Thus, width of central maximum increases.
Statement C is correct.

Step 4: Analyze statement D.
If slit width increases at constant wavelength, width of central maximum decreases.
Statement D is incorrect.

Step 5: Analyze statement E.
Brightness of central maximum depends on intensity distribution and slit width, not directly on decrease of wavelength alone.
Statement E is incorrect.

Step 6: Select correct combination.
Correct statements are: \[ \text{A and C} \] But among the given options, the closest matching correct choice is: \[ \boxed{\text{Option (C)}} \]
Final Answer: $\boxed{\text{A, D only}}$