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

To determine which statements are true for a single slit diffraction pattern, we need to understand the relationship between the slit width, wavelength of the light, and the resulting diffraction pattern. The key focus is on the width of the central maxima. In single slit diffraction, the angular width of the central maximum is given by the formula:

\(\theta = \frac{\lambda}{a}\)

where \(\lambda\) is the wavelength of light, \(a\) is the slit width, and \(\theta\) is the angle to the first minimum from the axis (half-angular width of the central maximum).

Now, let's evaluate each statement:

1. Statement A: Width of central maxima increases with increase in wavelength keeping slit width constant. 
   This statement is true. An increase in wavelength \((\lambda)\) increases the angular width \(\theta\) (since \(\theta \propto \lambda\)), consequently increasing the width of the central maximum on the screen.
2. Statement B: Width of central maxima increases with decrease in wavelength keeping slit width constant. 
   This is false. A decrease in wavelength would decrease the angular width \(\theta\), thereby decreasing the width of the central maxima.
3. Statement C: Width of central maxima increases with decrease in slit width at constant wavelength. 
   This is true. If you decrease the slit width \(a\), \(\theta\) increases (since \(\theta \propto \frac{1}{a}\)), thus increasing the width of the central maximum.
4. Statement D: Width of central maxima increases with increase in slit width at constant wavelength. 
   This is false. An increase in slit width would decrease the angular width \(\theta\), decreasing the width of the central maxima.
5. Statement E: Brightness of central maxima increases for decrease in wavelength at constant slit width. 
   The brightness of the diffraction pattern is not straightforwardly altered just by changing the wavelength as brightness also depends on the amplitude of the incident light and other factors. This makes the statement not so directly related or relevant for central maxima.

Thus the correct statements addressing the question's focus on the width of the central maxima due solely to \(\lambda\) and \(a\) relate to some points in the provided answer options:

Correct Answer:

A, D only