Chapter 31, Problem 21A

Dark and light fringes on the screen are produced by interference. In the following scenarios, a change is made to either the light source or the spacing d between slits A and B. Rank them by the distance between fringes, from greatest to least.

(A) Slit spacing d between A and B is reduced to 0.9d.

(B) Slit spacing d between A and B is increased to 1.1d.

(C) Wavelength of light is doubled.

To determine

To Rank: The distance between fringes from greatest to lowest.

Answer to Problem 21A

  $C>A>B$

Explanation of Solution

Introduction:

Interference of light can be defined as the superposition of two waves which are travelling along the same medium. The bending of light wave while encountering an obstacle can be defined as diffraction of light.

Due to interference, dark and bright fringes are produced on the screen. These bright and dark fringes occur from the different path lengths coming from the slits to the screen. When the slit spacing is smaller than the wavelength, the waves spread out widely and more diffraction occurs. Hence, distance between the fringes will be greatest in such case. On the other hand, when the slit spacing is greater than the wavelength, the distance between the fringes will be smaller.

Considering all the given cases, it can be concluded that in case C the wavelength is doubled, so the distance between the fringes will be greatest in this case. Similarly, in part A slit spacing is reduced, and in part B the slit spacing is increased which results in lesser distance between the fringes.

Hence, ranking of the distance between the fringes from greatest to least is given as:

  $C>A>B$

Conclusion:

Hence, the rank from greatest to least is $C>A>B$ .