12.2A Diffraction Gratings
1&2: Two slits are separated by a distance of 0.112 mm and are illuminated by 512 nm light. The interference pattern falls on a screen that is 4.80 m away.
1. What distance separates the fringes on the screen?
(2.19 cm)
2. What is the angle between the central maximum and the third order maximum?
(0.786o)
3. A single slit with a diameter of 0.0215 mm is illuminated by 550 nm light. What is the angle between the center of the central maximum, to the center of the first maximum on one side?
(2.20o)
4. A single slit has a width of 0.0450 mm and is illuminated by monochromatic light. A screen 1.85 m away has a central maximum pattern that is 2.10 cm wide. What is the wavelength of the light?
(255 nm)
5. A diffraction grating has 2450 lines per cm. It is illuminated by 632.8 nm light. What angle separates the first order and the fifth order fringes?
(50.82o - 8.92o = 41.9o)
Diffraction Questions from 12.2A (Worksheet 12.2A)
Young’s Double Slit:
1. Two slits are separated by a small distance and are illuminated by 575 nm light. The interference pattern has bright fringes that are 1.13 cm apart on a screen that is 2.46 m away. a. What distance separates the two slits? (0.125 mm) b. What is the angle between the second order and the fifth order fringes on one side? (0.790o) <Video a .:. Video b>
2. Two slits are separated by a distance of 0.245 mm and are illuminated by monochromatic light. The interference pattern has bright fringes separated by 1.41 cm and falls on a screen that is 5.59 m away. a. What is the wavelength of light? (618 nm) b. What is the distance on the screen between the central maximum and the fourth order maximum? (5.64 cm) <Video ab>
3. Two slits are separated by a distance of 0.251 mm and are illuminated by 647 nm light. The interference pattern has fringes separated by a distance of 1.52 cm on a screen some distance away. a. What is the distance to the screen? (5.90 m) b. What is the angle between the central maximum and the fourth order maximum? (0.591o) <Video ab>
4. Two slits are separated by a small distance and are illuminated by 478 nm light. The interference pattern has fringes separated by 1.65 cm on a screen that is 3.25 m away. a. What distance separates the slits? (9.42x10-5 m) b. What is the distance on the screen between the first order and the third order maximum on one side? (3.30 cm)
5. Two slits are separated by a distance of 0.280 mm and are illuminated by 652 nm light. The interference pattern falls on a screen that is 2.06 m away. a. What distance separates the fringes on the screen? (0.480 cm) b. What is the angle between the central maximum and the second order maximum? (0.267o)
Single Slit:
6. A single slit is illuminated by 460. nm light. The angular width of the central maximum is 1.20o. What is the width of the slit? (0.0439 mm) <Video>
7. A single slit has a width of 0.0680 mm and is illuminated by 715 nm light. What is the angle between the center of the central maximum, and the second minimum on one side? (0.904o) <Video>
8. A single slit has width of 0.0287 mm. There is an angle of 2.15o separating the center of the first maximum on one side with the center of the first maximum on the other side. What is the wavelength of light? (359 nm) <Video>
9. A single slit is illuminated by 656 nm light, and there is a 3.10o angle between the second maximum on one side, and the center of the central maximum. What is the width of the slit? (0.0303 mm) <Video>
10. A single slit has a width of 0.0243 mm, and there is a angle of 2.61o between the first maximum on one side, and the third minimum on the same side. What is the wavelength of the light? (738 nm) <Video>
11. A single slit has a width of 0.130 mm and is illuminated by monochromatic light. A screen 1.51 m away has a pattern where the center of the central maximum is separated from the center of the next maximum by a distance of 0.857 cm. What is the wavelength of light? (492 nm) ) <Video>
12. A single slit has a width of 0.113 mm and is illuminated by 635 nm light. The interference pattern is projected on a screen that is 4.51 m away. What is the distance on the screen from the center of the first maximum on the left side to the center of the first maximum on right side? (7.60 cm) <Video>
13. A single slit has a width of 0.0748 mm and is illuminated by 524 nm light. A screen some distance away has a central maximum pattern that is 3.24 cm wide. What is the distance to the screen? (2.31 m) <Video>
14. A single slit is illuminated by 524 nm light. A screen 4.20 m away has a central maximum pattern where the first minimum on one side is separated from the second by a distance of 1.26 cm. What is the width of the slit? (1.75x10-4 m) <Video>
15. A single slit has a width of 0.152 mm and is illuminated by 740 nm light. The interference pattern is projected on a screen that is 2.57 m away. What is the distance on the screen from the center of the central maximum to the center of the second maximum on one side? (3.13 cm) <Video>
Diffraction Gratings:
16. A diffraction grating has 6126 lines per cm. It is illuminated by a monochromatic light, and the central maximum and third order fringe are separated by 31.0o. What is the wavelength of the light? (280 nm) <Video>
17. A diffraction grating has 3852 lines per cm. It is illuminated by 398 nm ligh. What angle separates the second order and the fourth order fringes? (20.0o) <Video>
18. A diffraction grating is illuminated by 428 nm light. There is an angle of 3.58o between the central maximum and the second order fringe on one side. How many lines per cm does the grating have? (729 lines/cm) <Video>
19. A diffraction grating has 2083 lines/cm. It is illuminated by a monochromatic light beam. There is an angular separation of 8.13o between the central maximum and the first order fringe. What is the wavelength of light? (679 nm) <Video>
20. A diffraction grating is illuminated by a 596 nm light. There is an angle of 38.2o between the central maximum and the third order fringe on one side. How many lines per cm does the grating have? (3459 lines/cm) <Video>
The Practice Problems Solved: (This is old)
Worksheet 12.2A – Diffraction Gratings
12F1 – Young’s Double Slit
1. A parallel beam of light from a laser with a wavelength of 632.8 nm falls on two very narrow slits 0.0320 mm apart.
a. The bright fringes are 6.7 cm apart on a screen some distance away. What is the distance to the screen? (3.39 m)
b. What angle separates the central fringe, and the third order fringe? What distance is this on the screen? (3.40o, 20.1 cm)
2. Two narrow slits are separated by 0.0895 mm are illuminated by monochromatic light. The fringes on the screen 2.10 m away are 9.72 mm apart.
a. What is the wavelength of light? (414 nm)
b. What angle separates the central bright spot and the 4th order fringe? What distance is this on the screen? ( 1.06o, 3.89 cm)
3. Two slits make an interference pattern with 550. nm light on a screen that is 4.50 m away. The distance separating the third order fringe on the left from the third order on the right is 5.14 cm. What is the distance separating the slits? (2.89x10-4 m or 0.289 mm)
12F2 – Single Slit Diffraction
4. If 410. nm light falls on a slit 0.0320 mm wide,
a. What is the full angular width of the central diffraction peak? (0.0256 rad or 1.47o)
b. What is its width on a screen that is 3.60 m away? (9.22 cm)
c. What distance separates the central maximum from the next maximum on a screen 7.10 m away? (13.6 cm)
5. Light from a helium–neon laser passes through a narrow slit and is incident on a screen 5.20 m from the slit. The graph to the right shows the variation with distance x along the screen of intensity I of the light on the screen. The wavelength of the laser is 632.8 nm.
a. Determine the width of the slit. (1.01 mm)
b. What two changes would happen to the pattern if we were to increase this width? (central maximum: brighter, narrower)
b. What would happen to the pattern if we were to increase the wavelength of the light? (central maximum: broader, other maxima more spread out)
12F3 – Diffraction Gratings
6. A diffraction grating produces a third order spectral line at 23.0o for 815 nm light.
a. What is the distance between the slits or lines? (6.26x10-6 m)
b. How many lines are there per cm? (1598)
7. A diffraction grating has 640. lines per millimeter. It is illuminated by monochromatic light. There is an angle of 17.2o between the central maximum and the second order maximum on one side.
a. What is the distance between the slits or lines? (1.56x10-6 m)
b. What is the wavelength of light being used? (231 nm)
12O – Diffraction Grating Resolvance (This is old and not on the new curriculum for May 2025 and onwards ; - )
8. A diffraction grating is used to resolve two lines in a spectrum in the first order. The two lines have wavelengths of 632.185 nm and 631.341 nm. Determine the minimum number of slits in the grating that will enable the two lines to be resolved. (749 slits)
9. A 3.80 mm-wide beam of 432.7 nm light illuminates 1,112 slits in a diffraction grating.
a. What is the smallest difference in wavelength from this wavelength that the grating can resolve in the second order? (0.195 nm)
b. How many slits per cm does this grating have? (2930 lines per cm)
Practice for 12.2A (This is old)
Get the Document: PracticeFor12.2A-Diffraction.pdf
1. a-b: Two slits are separated by a small distance and are illuminated by 575 nm light. The interference pattern has bright fringes that are 1.13 cm apart on a screen that is 2.46 m away.
a. What distance separates the two slits? (0.125 mm) <Video a>
b. What is the angle between the second order and the fifth order fringes on one side? (0.790o) <Video b>
c. A single slit has a width of 0.130 mm and is illuminated by monochromatic light. A screen 1.51 m away has a pattern where the center of the central maximum is separated from the center of the next maximum by a distance of 0.857 cm. What is the wavelength of light? (492 nm) <Video>
d-e: A diffraction grating has 6126 lines per cm. It is illuminated by a monochromatic light, and the central maximum and third order fringe are separated by 31.0o.
d. What is the wavelength of the light? (280 nm) <Video>
e. What is the smallest difference in wavelength this grating can resolve in the first order given a beam that is 1.80 mm wide, and 423 nm light? (0.384 nm) <Video>
2. a-b: Two slits are separated by a distance of 0.245 mm and are illuminated by monochromatic light. The interference pattern has bright fringes separated by 1.41 cm and falls on a screen that is 5.59 m away.
a. What is the wavelength of light? (618 nm)
b. What is the distance on the screen between the central maximum and the fourth order maximum? (5.64 cm) <Video ab>
c. A single slit has a width of 0.113 mm and is illuminated by 635 nm light. The interference pattern is projected on a screen that is 4.51 m away. What is the distance on the screen from the center of the first maximum on the left side to the center of the first maximum on right side? (7.60 cm) <Video>
d-e: A diffraction grating has 3852 lines per cm. It is illuminated by a 398 nm light beam that is 2.50 mm wide.
d. What angle separates the second order and the fourth order fringes? (20.0o) <Video>
e. For what wavelength of light could this setup resolve a difference of 0.410 nm in the first order? (395 nm) <Video>
3. a-b: Two slits are separated by a distance of 0.251 mm and are illuminated by 647 nm light. The interference pattern has fringes separated by a distance of 1.52 cm on a screen some distance away.
a. What is the distance to the screen? (5.90 m)
b. What is the angle between the central maximum and the fourth order maximum? (0.591o) <Video ab>
c. A single slit has a width of 0.0748 mm and is illuminated by 524 nm light. A screen some distance away has a central maximum pattern that is 3.24 cm wide. What is the distance to the screen? (2.31 m) <Video>
d-e: A diffraction grating is illuminated by a 428 nm light beam that is 1.60 mm wide. There is an angle of 3.58o between the central maximum and the second order fringe on one side.
d. How many lines per cm does the grating have? (729 lines/cm) <Video>
e. What is the smallest difference in wavelength from 428 nm this setup can resolve in the first order? (3.67 nm) <Video>
4. a-b: Two slits are separated by a small distance and are illuminated by 478 nm light. The interference pattern has fringes separated by 1.65 cm on a screen that is 3.25 m away.
a. What distance separates the slits? (9.42x10-5 m)
b. What is the distance on the screen between the first order and the third order maximum on one side? (3.30 cm)
c. A single slit is illuminated by 524 nm light. A screen 4.20 m away has a central maximum pattern where the first minimum on one side is separated from the second by a distance of 1.26 cm. What is the width of the slit? (1.75x10-4 m)
d-e: A diffraction grating has a distance of 4.80x10-6 m between lines. It is illuminated by a monochromatic light beam. There is an angular separation of 8.13o between the central maximum and the first order fringe.
d. What is the wavelength of light? (679 nm)
e. How wide does the beam of light have to be to resolve the two wavelengths 421.171 nm and 421.201 nm in the second order using the same diffraction grating? (3.37 cm)
5. a-b: Two slits are separated by a distance of 0.280 mm and are illuminated by 652 nm light. The interference pattern falls on a screen that is 2.06 m away.
a. What distance separates the fringes on the screen? (0.480 cm)
b. What is the angle between the central maximum and the second order maximum? (0.267o)
c. A single slit has a width of 0.152 mm and is illuminated by 740 nm light. The interference pattern is projected on a screen that is 2.57 m away. What is the distance on the screen from the center of the central maximum to the center of the second maximum on one side? (3.13 cm)
d-e: A diffraction grating is illuminated by a 596 nm light. There is an angle of 38.2o between the central maximum and the third order fringe on one side.
d. How many lines per cm does the grating have? (3459 lines/cm)
e. How wide does the beam of light have to be to resolve the two wavelengths 512.174 nm and 512.286 nm in the first order using the same diffraction grating? (1.32 cm)