34. Wave Optics

In a double-slit experiment, let d = 5.00D = 40.0λ. Compare (as a ratio) the intensity of the third-order interference maximum with that of the zero-order maximum.

Monochromatic light falling on two slits 0.018 mm apart produces the fifth-order bright fringe at a 12° angle. What is the wavelength of the light used?

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?

In a two-slit interference pattern, the intensity at the peak of the central maximum is I₀. 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 (u = 0°) is I₀. What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to I₀/2?

(II) Light of wavelength λ passes through a pair of slits separated by 0.17 mm, forming a double-slit interference pattern on a screen located a distance 35 cm away. Suppose that the image in Fig. 34–9a is an actual-size reproduction of this interference pattern. Use a ruler to measure a pertinent distance on this image; then utilize this measured value to determine λ (nm) .

(II) Assume that light of a single color, rather than white light, passes through the two-slit setup described in Example 34–4. If the distance from the central fringe to a first-order fringe is measured to be 2.9 mm on the screen, determine the light’s wavelength (in nm) and color (see Fig. 34–11).

Imagine the following Young’s double-slit experiment using matter rather than light: electrons are accelerated through a potential difference of 18 V, pass through two closely spaced slits separated by a distance d, and create an interference pattern. (a) Using Example 37–11 and Section 34–3 as guides, find the required value for d if the first-order interference fringe is to be produced at an angle of 10°. (b) Given the approximate size of atoms, would it be possible to construct the required two-slit set-up for this experiment?

In a double-slit experiment, the slit separation is 200 times the wavelength of the light. What is the angular separation (in degrees) between two adjacent bright fringes?

Two 0.010-mm-wide slits are 0.030 mm apart (center to center). Determine (a) the spacing between interference fringes for 520-nm light on a screen 1.0 m away and (b) the distance between the two diffraction minima on either side of the central maximum of the envelope.

A 450 nm laser shines light through a double slit of 0.2 mm separation. If a screen is placed 4 m behind the double slit, how wide are the bright fringes of the diffraction pattern?

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?

Light of wavelength 474 nm in air shines on two slits 6.00 x 10^-2 mm apart. The slits are immersed in water, as is a viewing screen 60.0 cm away. How far apart are the fringes on the screen?