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 double-slit experiment

(b) Width of the spacing between two slits, d$=1.55\times {10}^{-4}\mathrm{m}$

Step-by-step solution

Double-slit experiment

It proposes that things we name particles, such as electrons, mix particle and wave characteristics in some way. This is quantum mechanics well-known wave-particle duality.

Find the Apertures is single-slit or Double-slit (part a)

Because the intensity of the light fringes drops slowly as the order of the fringes increases, and the fringes are evenly spaced, the given graph displays a pattern of double-slit experiment.

Find Width (part b)

In the double slit experiment, the position of the brilliant fringes can be written as follows:

$y_m=\frac{m\lambda L}{d}$

As a result, the distance between any two brilliant fringes is

$$\begin{gathered} \Delta y=y_{m+1}-y_m \\ =\frac{(m+1)\lambda L}{d}-\frac{m\lambda L}{d} \\ =\frac{\lambda L}{d} \end{gathered}$$

We may calculate the ratio by rearranging this equation.

$d=\frac{\lambda L}{\Delta y}$

The spacing in between two consecutive brilliant fringes is$1$cm, as seen in the diagram. hence

$d=\frac{\left(620\times {10}^{-9}\mathrm{m}\right)\times 2.5\mathrm{m}}{1\times {10}^{-2}\mathrm{m}}$

$d=1.55\times {10}^{-4}\mathrm{m}$