Chapter 40, Problem 16SP

Considering Young’s experiment using monochromatic light, what happens to the width of the central fringe (and, indeed, of all the fringes) if we decrease the wavelength by 10%, all else kept constant? Explain your answer. [Hint: The width of the central maximum is taken to be the separation between the centers of the first minima above and below the central axis.]

To determine

The effect on the width of the central fringe in the Young’s experiment using monochromatic light if the wavelength of the light is decreased by $10\%$ with all else kept constant.

Answer to Problem 16SP

Solution:

The w idth of all the fringes will decrease by $10\%$ .

Explanation of Solution

Given data:

The wavelength of the monochromatic light is decreased by $10\%$.

Formula used:

The expression for the fringe width of the fringe is written as

$\Delta y=\frac{s{\lambda }_0}{a}$

Here, $\Delta y$ is the fringe width of the fringes, $s$ is the distance between the slits and the screen, ${\lambda }_0$ is the wavelength of the monochromatic light, and $a$ is the separation between the slits.

Explanation:

Recall the expression for the fringe width:

$\Delta y=\frac{s{\lambda }_0}{a}$

Understand that for given young’s experiment, the value of the distance between the slits and the screen and the separation between the slits will be constant. Thus, fringe width will be directly proportional to the wavelength of the fringe.

$\Delta y\propto {\lambda }_0$

The above expression shows that the $10\%$ decrease in the wavelength of the monochromatic light results in the $10\%$ decrease in the width of the central fringe and also the width of the all fringes as they are directly proportional to each other.

Conclusion:

Hence, the width of the all the fringes are decreased by $10\%$.