Question

FIGURE shows the light intensity on a screen $2.5m$behind an aperture. The aperture is illuminated with light of wavelength $620nm$.

a. Is the aperture a single slit or a double slit? Explain.

b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

Short answer

(a) The Aperture is a single-slit

(b) Aperture distance of Spacing between the slits,$a=155\mu m$

Step-by-step solution

Single-slit experiment

In a single slit experiment, monochromatic light is sent via a single slit of finite width, and an identical pattern appears on the screen. The width and intensity of the single-slit diffraction pattern decrease as we go away from the central maximum, unlike the double-slit diffraction pattern.

Find the aperture is single-slit or double-slit (part a)

Because the intensity of the center bright spot is significantly more than that of the secondary maxima, and the central bright spot's breadth is similarly greater than that of the secondary maxima, the presented graph indicates a single-slit experiment pattern.

Find spacing between the slits (part b)

The position of the black fringes in the case of a single slit is given as

$y_p=\frac{pL\lambda }{a}$

Looking at the figure, we can see that the first black fringe is $1$cm away from the center of the primary brilliant point. As a result, given the assumption that$y_1=1\mathrm{cm}$, we may rearrange the previous equation to compute the width of the slit a.

$$\begin{gathered} a=\frac{L\lambda }{y_1} \\ =\frac{(2.5\mathrm{m})\times 620\times {10}^{-9}\mathrm{m}}{1\times {10}^{-2}\mathrm{m}} \end{gathered}$$

$a=155\mu \mathrm{m}$