# 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.

Q1:

A diffraction grating has 2,000 lines per centimeter. At what angle will the first-order maximum for a green light with a wavelength of 520 nm be?

Q2:

Light of wavelength 470 nm is incident on a diffraction grating. The first-order maximum of the diffraction pattern produced occurs at an angle of . How many lines per centimeter are there on the diffraction grating?

• A
• B
• C
• D
• E

Q3:

Structures on a bird feather act like a reflection grating having 8,000 lines per centimeter. What is the angle of the first-order maximum for 600 nm light incident on these structures?

Q4:

Calculate the wavelength of light that has its second-order maximum at when falling on a diffraction grating that has 5,000 lines per centimeter.

Q5:

A diffraction grating produces a second maximum that is 89.7 cm from the central maximum on a screen 2.0 m away. If the grating has 600 lines per centimeter, what is the wavelength of the light that produces the diffraction pattern?

Q6:

How many complete orders of the visible spectrum can be produced with a diffraction grating that contains 5,000 lines per centimeter? Use a range of 400 nm to 700 nm as corresponding to the visible spectrum.

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?

Q8:

An opal acts like a reflection grating with rows separated by about 8.0 μm.

If the opal is illuminated normally, at what angle will 700 nm light be seen?

If the opal is illuminated normally, at what angle will 460 nm light be seen?

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

Q10:

A hydrogen gas discharge lamp emits visible light at wavelength . Light from this lamp falls on a diffraction grating with a slit separation of 0.0250 mm. How far from the central maximum is the third maxima when viewed on a screen 2.00 m from the slits?

Q11:

A hydrogen gas discharge lamp emits visible light at wavelength . Light from this lamp falls on a diffraction grating with a slit separation of 0.0250 mm. How far from the central maximum is the third maxima when viewed on a screen 2.00 m from the slits?

Q12:

A hydrogen gas discharge lamp emits visible light at wavelength . Light from this lamp falls on a diffraction grating with a slit separation of 0.0250 mm. How far from the central maximum is the third maxima when viewed on a screen 2.00 m from the slits?

Q13:

A hydrogen gas discharge lamp emits visible light at wavelength . Light from this lamp falls on a diffraction grating that has a slit separation of 0.025 mm. By what distance are the second and third maxima separated when viewed on a screen 2.0 m from the slits?

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

Q15:

A hydrogen gas discharge lamp emits visible light at wavelength of m. Light from this lamp falls on a diffraction grating with slits separated by 0.0250 mm. How far from the central maximum is the third maximum when viewed on a screen 2.00 m from the slits?

Q16:

Find the angle for the fourth-order maximum produced by 580 nm wavelength yellow light falling on a diffraction grating having 1,630 lines per centimeter.

Q17:

A diffraction grating produces a third-order maximum for 760 nm red light at an angle of . What is the line-spacing distance on the grating?

Q18:

An electric current through a gas produces a wavelength of visible light. What is the wavelength produced if it forms a first-order maximum at an angle of when projected on a diffraction grating having 11,000 lines per centimeter?

Q19:

The spacing between structures in a feather acts as a reflection grating, producing a third-order maximum for 560 nm light at a angle. What is the distance between these structures?

Q20:

At what angle does a diffraction grating produce a second-order maximum for light having a first-order maximum at ?

Q21:

What is the longest wavelength for which a diffraction grating with lines per centimeter will produce a second-order maximum?

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

Q23:

A grating with 3,900 lines per centimeter is used to diffract light that contains all wavelengths between 450 nm and 650 nm. How wide is the first-order spectrum on a screen 3.00 m from the grating?

Q24:

A diffraction grating produces a first-order maximum for the shortest wavelength of visible light at . Find the angle at which the first-order maximum will have the largest wavelength of visible light. Use wavelengths from 390 nm to 770 nm for the range of visible light.

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