Students will learn about diffraction of light and the interference patterns that are produced through constructive and destructive interference of the waves. Students will also learn to calculate diffraction pattern spacing or work backwards to calculate the wavelength of light emitted.

### Key Equations

Double slit interference maxima.

Single slit interference maxima.

Diffraction grating interference maxima.

Thin film interference:

- Waves are characterized by their ability to constructively and destructively
*interfere*. Light waves which interfere with themselves after interaction with a small aperture or target are said to*diffract*.

- Light creates interference patterns when passing through holes (“slits”) in an obstruction such as paper or the surface of a CD, or when passing through a thin film such as soap.

#### Example 1

A typical experimental setup for an interference experiment will look something like this:

Definitions:

**Maximum** = place where waves constructively interfere

**Minimum** = place where waves destructively interfere

Because the screen distance *L* is much larger than the slit distance *d*, one can see that

Thus, the condition for a first maximum becomes

One can now easily calculate where the first maximum should appear if given the wavelength of the laser light, the distance to the screen and the distance between slits.

First Maximum:

#### Example 2

White light (which is comprised of all wavelengths and thus all colors) separates into a rainbow pattern as shown below.

Each wavelength of light has a unique interference pattern given by the equation above. Thus all the wavelengths (i.e. colors) have a unique

### Watch this Explanation

### Simulation

Wave Interference (PhET Simulation)

### Explore More

- In your laboratory, light from a
650nm laser shines on two thin slits. The slits are separated by0.011mm . A flat screen is located1.5m behind the slits.- Find the angle made by rays traveling to the third maximum off the optic axis.
- How far from the center of the screen is the third maximum located?
- How would your answers change if the experiment was conducted underwater?

- Again, in your laboratory,
540nm light falls on a pinhole0.0038mm in diameter. Diffraction maxima are observed on a screen5.0m away.- Calculate the distance from the central maximum to the first interference maximum.
- Qualitatively explain how your answer to (a) would change if you:
- move the screen closer to the pinhole
- increase the wavelength of light
- reduce the diameter of the pinhole

- Students are doing an experiment with a Helium-neon laser, which emits
632.5nm light. They use a diffraction grating with8000 lines/cm. They place the laser1m from a screen and the diffraction grating, initially,95cm from the screen. They observe the first and then the second order diffraction peaks. Afterwards, they move the diffraction grating closer to the screen.- Fill in the
**Table**(below) with the*expected*data based on your understanding of physics. Hint: find the general solution through algebra*before*plugging in any numbers. - Plot a graph of the first order distance as a function of the distance between the grating and the screen.
- How would you need to manipulate this data in order to create a
*linear*plot? - In a real experiment what could cause the data to deviate from the expected values? Explain.
- What safety considerations are important for this experiment?
- Explain how you could use a diffraction grating to calculate the unknown wavelength of another laser.

Distance of diffraction grating to screen (cm) Distance from central maximum to first order peak (cm) 95 75 55 35 15 - Fill in the
- A crystal of silicon has atoms spaced
54.2nm apart. It is analyzed as if it were a diffraction grating using anx− ray of wavelength12nm . Calculate the angular separation between the first and second order peaks from the central maximum. - Laser light shines on an oil film
(n=1.43) sitting on water. At a point where the film is96nm thick, a1st order dark fringe is observed. What is the wavelength of the laser? - You want to design an experiment in which you use the properties of thin film interference to investigate the variations in thickness of a film of water on glass.
- List all the necessary lab equipment you will need.
- Carefully explain the procedure of the experiment and draw a diagram.
- List the equations you will use and do a sample calculation using realistic numbers.
- Explain what would be the most significant errors in the experiment and what effect they would have on the data.

#### Answers to Selected Problems

- a.
10.2∘ b.27cm c.20cm - a.
0.72m -
54cm,44cm,21cm,8.8cm -
13.5∘ -
549nm - .