34. Wave Optics

A 532 nm laser illuminates a pair of slits separated by $70\mu \mathrm{ m}$. What is the angular separation, in degrees, between the $m=1$ and $m=2$ bright fringes?

In a two-slit experiment, laser light of wavelength  $600\mathrm{nm}$ passes through a pair of slits separated by $42\mu \mathrm{m}.$ If the observing screen is $1.4\mathrm{m}$ from the slits, what is the separation, in mm, between the bright fringes?

A $532\mathrm{nm}$ laser illuminates a pair of slits separated by $70\mathrm{\mu }\mathrm{m}$. What is the angular separation, in degrees, between the m = 1 and m = 2 bright fringes?

In a two-slit experiment, laser light of wavelength $600\mathrm{nm}$ passes through a pair of slits separated by $42\mathrm{\mu }\mathrm{m}$. If the observing screen is $1.4\mathrm{m}$ from the slits, what is the separation, in mm, between the bright fringes?

Light of wavelength 550 nm illuminates a double slit, and the interference pattern is observed on a screen behind the slit. The third maximum is measured to be 3.0 cm from the central maximum. The slits are then illuminated with light of wavelength 440 nm. How far is the fourth maximum from the central maximum?

A double-slit experiment is set up using a helium-neon laser (λ=633 nm). Then a very thin piece of glass (n=1.50) is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the m=10 dark fringe. How thick is the glass?

Coherent light with wavelength 450 nm falls on a pair of slits. On a screen 1.80 m away, the distance between dark fringes is 3.90 mm. What is the slit separation?

Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between the second and third dark lines of the interference pattern on the screen when the slits are illuminated with coherent light with a wavelength of 500 nm?

Coherent light of frequency 6.32 * 1014 Hz passes through two thin slits and falls on a screen 85.0 cm away. You observe that the third bright fringe occurs at ±3.11 cm on either side of the central bright fringe. (a) How far apart are the two slits? (b) At what distance from the central bright fringe will the third dark fringe occur?

In a two-slit interference pattern, the intensity at the peak of the central maximum is I0. (a) At a point in the pattern where the phase difference between the waves from the two slits is 60.0°, what is the intensity?

Two slits spaced 0.260 mm apart are 0.900 m from a screen and illuminated by coherent light of wavelength 660 nm. The intensity at the center of the central maximum 1u = 0°2 is I0. What is the distance on the screen from the center of the central maximum (a) to the first minimum

Two slits spaced 0.260 mm apart are 0.900 m from a screen and illuminated by coherent light of wavelength 660 nm. The intensity at the center of the central maximum 1u = 0°2 is I0. What is the distance on the screen from the center of the central maximum (b) to the point where the intensity has fallen to I0>2?

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 5.00x10^-4 W/m2, what is the intensity at a point on the screen that is 0.900 mm from the center of the central maximum?

Laser light of wavelength 500.0 nm illuminates two identical slits, producing an interference pattern on a screen 90.0 cm from the slits. The bright bands are 1.00 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.

FIGURE CP33.73 shows two nearly overlapped intensity peaks of the sort you might produce with a diffraction grating (see Figure 33.9b). As a practical matter, two peaks can just barely be resolved if their spacing Δy equals the width w of each peak, where w is measured at half of the peak’s height. Two peaks closer together than w will merge into a single peak. We can use this idea to understand the resolution of a diffraction grating. a. In the small-angle approximation, the position of the m=1 peak of a diffraction grating falls at the same location as the m=1 fringe of a double slit: y1=λL/d. Suppose two wavelengths differing by Δλ pass through a grating at the same time. Find an expression for Δy, the separation of their first-order peaks.