# Lesson 18: Diffraction and Interference!

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1 Lesson 18: Diffraction and Interference Part 1: The Double Slit Experiment What is light? - A particle? - A wave? In 1801, Thomas Young s Double Slit Experiment confirmed the wave nature of light: If light is a particle: But this is what showed on the screen instead Light source Shone through a sheet with two slits cut into it Light appears on the screen behind Why? Light s wave nature. Diffraction:

2 Interference: Standing waves: Fringe Pattern The pattern on the screen is a standing wave of light. A standing wave is produced when two identical waves meet and interfere with each other. This results in peaks, where the waves reinforce each other, and areas with no wave at all where they cancel each other out.

3 Part 2: Two Double Slit Formulas When light is shone through two or more slits, an interference pattern will always be observed. Antinodes Nodes: Formula:

4 Example: A student doing Young s Experiment finds that the distance between the central fringes and the seventh nodal line is 6.0 cm. If the screen is 3.0 m from the slits, whose separation distance is 220 µm, what is the wavelength used? Another formula Example: If a yellow light with a wavelength of 540 nm shines on a double slit with a slit separation distance of 2.20µm apart, determine the angle of the second bright fringe.

5 Part 3: Diffraction Gratings A diffraction grating uses multiple parallel slits, evenly spaced, to show an interference pattern. The two formulas can still be used: Except often you will be given line density and you will need to use this to find the line spacing (d). Example: A monochromatic light source shines on a diffraction grating of lines/cm and produces a first order antinode 65 cm off the centre line on a screen 100 cm away. What is the wavelength shone? All of the examples so far have used monochromatic (single wavelength) light. If white light (all visible wavelengths) is used, the diffraction grating will separate it into a continuous, rainbow, spectrum since each wavelength diffracts differently. Rule:

6 Practice Problems: 1. Light falls on a pair of slits 1.28 x 10-5 m apart. The maxima are 4.11 x 10-2 m apart and the screen is 1.00 m from the slits. What is the wavelength of the light? [5.26 x 10-7 m] 2. Yellow light of wavelength 615 nm is incident on a double slit where slits are 1.3 mm apart. At what angle will the fifth order antinodal line appear? (0.14 o ) 3. Light of frequency 6.09 x Hz is incident on a pair of straight parallel slits and produces an interference pattern on a screen 7.0 m away. If the fringe spacing on the screen is 2.5 cm, determine the distance between the slits. (0.138 mm) 4. Light of frequency 4.8 x Hz is incident on a pair of straight parallel slits where the slits are 0.16 mm apart. It creates an interference pattern on a screen 8.0 m away. What is the distance from the centre of the pattern to the fourth bright line? (0.13 m) 5. Light of an unknown wavelength is incident on two slits separated by 0.20 mm. The second bright fringe is located at an angle of 0.26 o from the central antinode. What is the light s wavelength? [4.5 x 10-7 m] 6. Blue light of 460 nm is incident on two slits that are 0.55 mm apart. What is the angle of diffraction for the third antinodal line? [0.14 o ] 7. The second nodal line of an interference pattern occurs at o relative to the central antinode. The two slits are separated by 0.40 mm. What is the wavelength and colour of light producing this pattern? [4.4 x 10-7 m, violet] 8. Monochromatic light is incident on two slits separated by 0.15 mm. An interference pattern is observed on a screen 5.0 m away. The distance between the 3rd dark fringe and the central antinode is 4.50 x 10-2 m. What is the wavelength of the light? [5.4 x 10-7 m] 9. Monochromatic light is incident on two slits separated by 3.00 x 10-5 m. The distance between antinodes is 3.10 x 10-2 m. If the screen is 1.50 m from the slits, what is the light s colour and wavelength? [6.20 x 10-7 m, red] 10. A student used light of wavelength 5.00 x 10-7 m and found that the distance between the third node and the central antinode was 1.00 x 10-1 m. If the screen was located 1.20 m away from the slits, how far apart are the slits? [1.50 x 10-5 m] 11. Green light of wavelength 5000 Å (1 Å = m) is shone on a grating and a second order image is produced at 32 o. How many lines/cm are marked on the grating? (5300 lines/cm) 12. How many lines per metre does a diffraction grating have if the 2 nd order minimum occurs at an angle of deviation of 16.0 o when 530 nm light is used? (3.47 x 10 5 lines/m) nm yellow light is incident on a diffraction grating which has 150 lines/cm. What is the spacing between the bright fringes produced as a result on a screen 4.9 m away? (4.8 cm) 14. Light of frequency 5.0 x Hz falls on a diffraction grating which has 4.2 x 10 3 lines /cm. At what angle will the third antinodal line will be inclined to the forward direction? (49 o ) 15. A light ray of frequency 5.0 x Hz is incident on a diffraction grating that has 180 lines/cm. After passing through the grating the light travels 4.0 m in a trough of water to a screen where it produces an interference pattern. How far apart are the bright fringes on the screen? (3.2 cm) 16. The wavelength of a laser beam used in a compact disc player is 790 nm. Suppose that a diffraction grating produces first-order tracking beams which are 1.2 mm apart at a distance of 3.0 mm from the grating. Estimate the spacing between the slits of the grating. (2.0 x 10-6 m) 17. Monochromatic light with a frequency of 5.50 x Hz is directed onto a diffraction grating ruled with 6000 lines/m. What is the distance between the 3 rd bright band and the 5 th dark band of the interference pattern formed on a screen 2.50 m from the grating? (1.23 cm) 18. A student using a diffraction grating ruled with 6.20 x 10 4 lines/m to measure the frequency of some monochromatic light. If the nodal lines are m apart at a distance of 1.50 m from the grating, what is the frequency of the light used? (5.3 x Hz)

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