Chapter 36, Problem 1Q

You are conducting a single-slit diffraction experiment with light of wavelength λ. What appears, on a distant viewing screen, at a point at which the top and bottom rays through the slit have a path length difference equal to (a) 5λ and (b) 4.5λ?

To determine

To find:

a) What appears on a distant viewing screen at a point at which the top and bottom rays through the slit have a path length difference equal to $5\lambda .$

b) What appears on a distant viewing screen at a point at which the top and bottom rays through the slit have a path length difference equal to $4.5\lambda .$

Answer to Problem 1Q

Solution:

a) $m=5$ minimum.

b) Maximum between the $m=4$ and $m=5$ (approximately).

Explanation of Solution

1) Concept:

Usingthe condition for occurrence of minimum in a single slit experiment, we can find what appears on a distant viewing screen at a point at which the top and bottom rays through the slit have a path length difference equal to $5\lambda and 4.5\lambda .$

2) Formula:

$∆L=m\lambda$

3)  Given:

The single slit experiment is conducted with the light of wavelength $\lambda .$

4) Calculations:

a) In the single slit experiment, the condition for occurrence of minimum is

$Path length difference=∆L=m\lambda$ $For m=\mathrm{1,2},3$

From this, we can interpret that at $∆L=5\lambda ; m=5$ minimum appears.

b) $∆L=4.5\lambda$ implies that it corresponds to approximately maximum between $m=4 minimum and m=5 minimum.$

Conclusion:

We can predict about what appears on screen in a single slit experiment from the condition for minimum.