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.

Which of the following are true for a single slit diffraction

Q. 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) B, D only

(B) A, D only

(D) B, C only

Correct Answer: A, C, E only

Explanation

In single slit diffraction, the angular width of the central maxima is given by

$$ \theta = \frac{2\lambda}{a} $$

where $\lambda$ is the wavelength of light and $a$ is the slit width.

From the expression, the width of the central maxima is directly proportional to wavelength.

Hence, when wavelength increases at constant slit width, the width of central maxima increases. Therefore, statement A is correct and statement B is incorrect.

The width of central maxima is inversely proportional to slit width.

So, when slit width decreases at constant wavelength, the width of central maxima increases. Hence, statement C is correct and statement D is incorrect.

Brightness of central maxima is proportional to the square of amplitude and depends on the amount of light energy concentrated in the central region.

For a given slit width, decrease in wavelength results in less spreading of light and higher concentration of intensity at the center, thereby increasing brightness.

Thus, statement E is also correct.

Therefore, the correct set of statements is

A, C and E only.

Explanation

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