Chapter 26: Diffraction and Interference of Light

I. DiffractionA. Young’s two-slit experiment

• Interference fringes: the pattern of dark and light bands on a screen due to constructive and destructive interference of light waves passing through two narrow, closely spaced slits

• Monochromatic light: light of only one wavelength• Coherent waves: waves that are in phase--the wave crests and troughs reach the same

point at the same timeB. Diffraction of white light

• Constructive interference occurs in a bright, central band. Destructive interference occurs between the bright bands where its dark.

• When white light is used in a double-slit experiment, diffraction causes the appearance of colored spectra instead of bright and dark bands.

• The positions of the constructive and destructive interference bands depend on the wavelength of the light. All wavelengths interfere constructively in the central bright band, so that band is white.

II. Measuring the Wavelength of a Light Wave• (x) / (L) = (λ) / (d) • The distance between the first bright band and the central band is x.• The distance between the screen and the slits is L.• (See diagram on next page)

Eli Nobler--Chapter 26

III.Single-Slit DiffractionA. From one to many slits

• Light passing through a narrow hole or slit is diffracted, or spread from a straight-line path, and produces a diffraction pattern on a screen.

B. Measuring a wavelength of light• Both interference and diffraction patterns depend on the wavelength of light, the width

or separation of the slits, and the distance to the screen. • Interference patterns are narrower and sharper than diffraction patterns.

IV.Applications of DiffractionA. Diffraction Gratings

• Diffraction grating: a device with parallel ridges that reflects light and forms an interference pattern

• Consist of large numbers of slits and produce narrow interference patterns• Can be used to measure the wavelength of light precisely or to separate light composed

of different wavelength B. Resolving Power of Lenses

• Raleigh criterion: when the central bright band of one star falls on the first dark band of the second, the two stars will be just resolved

• Diffraction limits the ability of a lens to distinguish two closely spaced objects

Practice QuestionsMultiple Choice1. An argon ion laser with a wavelength of 476.5 nm is used as a light source in a

double slit experiment. If the slits are 0.0190 mm apart and the screen is 0.800 m away, what is the separation between the central bright line and the first-order bright line?

A) 21.3 mm B) 20.1 mm CORRECT C) 19.1 mm D) 18.6 mm

Eli Nobler--Chapter 26

2. What is the wavelength of light traveling through a diffraction grating on a spectrometer with 714 nm between lines and an angle of 54.0 degrees?

A) 578 nm CORRECT B) 420 nm C) 524 nm D) 505 nm3. Bright bands in interference fringes result from _____________. A) Destructive interference B) Constructive diffraction C) Destructive diffraction D) Constructive interference CORRECT4. In a double slit experiment with slits 1.0 x 10-5 m apart, light casts the first bring

band 3.0 x 10-2 m from the center of a screen 0.65 m away. What is the wavelength of this light?

A) 430 nm B) 390 nm C) 510 nm D) 460 nm CORRECT5. If white light passes through a grating spectroscope, you will see ______. A) A series of spectra CORRECT B) No spectrum C) Only on spectrum D) A spectrum of white lightFree-Response1. In a double-slit experiment, physics students use a laster with a known

wavelength of 632.8 nm. The slit separation is unknown. A student places the screen 1.000 m form the slits and finds the first-order line 65.5 mm from the central line. What is the slit separation?

2. Monochromatic green light of wavelength 546 nm falls on a single slit with width 0.095 mm. The slit is located 75 cm from a screen. How far from the center of the central band is the first dark band?

3. When two equally intense, coherent light waves are in phase at a point in space, the total intensity is four times the intensity of each of the waves alone--more than the sum of the intensities of the two waves. Explain why this does not violate the principle of conservation of energy.

4. When unpolarized light is normally incident on a plane surface, is there any possibility that the reflected light will be polarized? Explain.

5. Two narrow slits, illuminated by light consisting of two distinct wavelengths, produce two overlapping colored interference patterns on a distant screen. The center of the fourth bright fringe in one pattern coincides with the center of the third bright fringe in the other pattern. What is the ratio of the two wavelengths?

Eli Nobler--Chapter 26

ANSWER KEY TO PRACTICE PROBLEMS!!!!

Multiple Choice:1. B2. A3. D4. D5. A

FREE-RESPONSE:

1. 9.66 µm2. 4.3 mm3. The total energy equals the sum of the energy in the separate waves, but energy

is redistributed, greater where interference is constructive and less where it is destructive.

4. No. All directions perpendicular to the direction of wave motion are physically equivalent. There is nothing to distinguish a polarization direction.

5. 4/3

Eli Nobler--Chapter 26