# Worksheet: Diffraction Gratings

In this worksheet, we will practice calculating the characteristics of an interference pattern produced by visible light incident on a diffraction grating.

**Q7: **

A diffraction grating with 2,000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube.

At what angle will you find the maxima of the first-order blue line of wavelength 410 nm?

At what angle will you find the maxima of the first-order blue line of wavelength 434 nm?

The maximum of another first-order line is found at . What is the wavelength of this line?

The maximum of another first-order line is found at . What is the wavelength of this line?

**Q9: **

A diffraction grating has a slit separation that is comparable to the wavelength of the light passing through the grating’s slits. The grating has 125 lines per centimeter and the light that it diffracts has a wavelength of 600 nm. The diffracted light is incident on a screen that is at a distance from the grating. Assume that the distance between adjacent fringes is . What is the distance between fringes produced by this diffraction grating?

- A m
- B m
- C m
- D m
- E m

**Q14: **

A laser beam shining light of wavelength 632.8 nm is reflected from the surface of a CD onto a wall. The brightest spot on the wall is from the reflected beam, at an angle equal to the angle of incidence of laser light onto the CD, but a fringe pattern is also observed. The wall is 1.50 m from the CD, and the first fringe is 0.600 m from the central maximum. What is the spacing of grooves on the CD?

- A m
- B m
- C m
- D m
- E m

**Q22: **

The yellow light from a light source appears to the human eye to be monochromatic, but it produces two first-order maxima at and when projected onto a 12,000-lines-per-centimeter diffraction grating. What are the two wavelengths of the light that produce these respective maxima angles?

- A390.2 nm and 390.5 nm
- B500.2 nm and 500.5 nm
- C479.2 nm and 479.5 nm
- D450.2 nm and 450.5 nm
- E600.2 nm and 600.5 nm

**Q25: **

The movable mirror of a Michelson interferometer is attached to one end of a thin metal rod of length 26 mm. The other end of the rod is anchored so it does not move. As the temperature of the rod changes from to , a change of 12 fringes is observed. The light source is a He-Ne laser with a wavelength of 633 nm.

What is the change in length of the metal bar?

- A3.8 μm
- B4.5 μm
- C1.9 μm
- D2.5 μm
- E3.3 μm

What is the thermal expansion coefficient of the metal in the bar?

- A
- B
- C
- D
- E