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Physics 214 - Prelab 1

Interference and Diffraction

Name:

Section:

Date:

Your TA will collect this paper at the beginning of your lab section.

The basic problem is shown in the following figure, which represents light of a given wavelength \(\lambda\) passing through two slits separated by a distance \(d\). The distance to the screen is \(L\). In this lab experiment you will measure the intensity at a position \(y\) along the screen, which corresponds to a scattering angle \(\theta\).

../_images/214_prelab_1_fig_1.png

Fig. 5 Fig. 1

As shown in class, the phase difference between the two light beams at position \(y\) is:

\[ \phi = 2\pi(\delta/\lambda)\]

$$

is the path difference between the two beams. From phasor analysis, if the intensity arriving at the screen from each slit is \(I_1\), the total intensity at \(y\) from both slits is:

\[ I = 4I_1\cos^2\frac{\phi}{2} = 4I_1\cos^2\left(\frac{\pi d}{\lambda L}y\right) \]
../_images/214_prelab_1_fig_2.png

Fig. 6 Fig. 2

The more general form for the interference pattern from \(N\) slits is:

\[ I = I_1\left(\frac{\sin(N\phi/2)}{\sin(\phi/2)}\right)^2. \]

1.

Show that this reduces to the 2-slit case when \(N = 2\).

When we consider the diffraction of light through a single slit of width a, we find that the single-slit intensity, \(I_1\), in the above equation is not simply a constant but also depends on angle. The single-slit pattern looks like the following plot:

../_images/214_prelab_1_fig_3.png

Fig. 7 Fig. 3

Answer:

2.

Calculate the position of the first diffraction minimum assuming a laser wavelength of 633 nm, a slit width of 20 \(\mu\)m, and a screen distance of 1 m.

\[ y = \_\_\_\_ \]

Answer:

!!DO NOT FORGET TO INDICATE UNITS FOR ALL NUMERICAL ANSWER YOU PROVIDE!!

So the net result due to both interference and diffraction is the product of the curves in Figs. 2 and 3 (see also 214 Lecture 3):

3.

../_images/214_prelab_1_fig_4.png

Fig. 8 Fig. 4

You should be able to tell what the ratio \(d/a\) is by just looking at the above pattern.

\[ d/a = \_\_\_\_ \]

Answer:

Explain your method:

Physics 214 Prelab 1 Fall 2020 Edition

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Physics 214 - Prelab 1