Chapter 36

Monochromatic light of wavelength $\lambda$ = 620 nm from a distant source passes through a slit 0.450 mm wide. The diffraction pattern is observed on a screen 3.00 m from the slit. In terms of the intensity $I_0$ at the peak of the central maximum, what is the intensity of the light at the screen the following distances from the center of the central maximum: (a) 1.00 mm; (b) 3.00 mm; (c) 5.00 mm?

A slit $0.240\mathrm{mm}$ wide is illuminated by parallel light rays of wavelength $540\mathrm{nm}.$ The diffraction pattern is observed on a screen that is $3.00\mathrm{m}$ from the slit. The intensity at the center of the central maximum $(\theta =0^{\circ })$ is $6.00\times {10}^{-6}\mathrm{W}/{\mathrm{m}}^2$. (a) What is the distance on the screen from the center of the central maximum to the first minimum? (b) What is the intensity at a point on the screen midway between the center of the central maximum and the first minimum?

Monochromatic light of wavelength 592 nm from a distant source passes through a slit that is 0.0290 mm wide. In the resulting diffraction pattern, the intensity at the center of the central maximum $(\theta =0^{\circ })$ is 4.00 $\times$ 10${}^{-5}$ W/m${}^2$. What is the intensity at a point on the screen that corresponds to $\theta$ = 1.20${}^{\circ }$?

A single-slit diffraction pattern is formed by monochromatic electromagnetic radiation from a distant source passing through a slit 0.105 mm wide. At the point in the pattern 3.25${}^{\circ }$ from the center of the central maximum, the total phase difference between wavelets from the top and bottom of the slit is 56.0 rad. (a) What is the wavelength of the radiation? (b) What is the intensity at this point, if the intensity at the center of the central maximum is $I_0$?

Parallel rays of monochromatic light with wavelength 568 nm illuminate two identical slits and produce an interference pattern on a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm. If the intensity at the center of the central maximum is 5.00 $\times$ 10${}^{-4}$ W/m${}^2$, what is the intensity at a point on the screen that is 0.900 mm from the center of the central maximum?

An interference pattern is produced by light of wavelength 580 nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of 0.530 mm. (a) If the slits are very narrow, what would be the angular positions of the first-order and second-order, two-slit interference maxima? (b) Let the slits have width 0.320 mm. In terms of the intensity $I_0$ at the center of the central maximum, what is the intensity at each of the angular positions in part (a)?

Laser light of wavelength $500.0\mathrm{nm}$ illuminates two identical slits, producing an interference pattern on a screen $90.0\mathrm{cm}$ from the slits. The bright bands are $1.00\mathrm{cm}$ apart, and the third bright bands on either side of the central maximum are missing in the pattern. Find the width and the separation of the two slits.

When laser light of wavelength 632.8 nm passes through a diffraction grating, the first bright spots occur at $\pm$17.8${}^{\circ }$ from the central maximum. (a) What is the line density (in lines/cm) of this grating? (b) How many additional bright spots are there beyond the first bright spots, and at what angles do they occur?

Monochromatic light is at normal incidence on a plane transmission grating. The first-order maximum in the interference pattern is at an angle of 11.3${}^{\circ }$. What is the angular position of the fourth-order maximum?

If a diffraction grating produces its third-order bright band at an angle of 78.4${}^{\circ }$ for light of wavelength 681 nm, find (a) the number of slits per centimeter for the grating and (b) the angular location of the first-order and second-order bright bands. (c) Will there be a fourth-order bright band? Explain.