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.
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.
A typical experimental setup for an interference experiment will look something like this:
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.
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
- In your laboratory, light from a
650nmlaser shines on two thin slits. The slits are separated by 0.011mm. A flat screen is located 1.5mbehind 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,
540nmlight falls on a pinhole 0.0038mmin diameter. Diffraction maxima are observed on a screen 5.0maway.
- 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
632.5nmlight. They use a diffraction grating with 8000lines/cm. They place the laser 1mfrom a screen and the diffraction grating, initially, 95cmfrom 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
- A crystal of silicon has atoms spaced
54.2nmapart. It is analyzed as if it were a diffraction grating using an x−ray of wavelength 12nm. 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 is 96nmthick, a 1storder 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
10.2∘b. 27cmc. 20cm