Two narrow slits separated by 1.4 mm are illuminated by 544-nm light. Find the distance between adjacent bright fringes on a screen 5.0 m from the 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. 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.

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?

(II) If 720-nm and 660-nm light passes through two slits 0.61 mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.0 m away?

A parallel beam of light from a He–Ne laser, with a wavelength 633 nm, falls on two very narrow slits 0.068 mm apart. How far apart are the fringes in the center of the pattern on a screen 4.2 m away?

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?

In a two-slit interference experiment, the path length to a certain point P on the screen differs for one slit in comparison with the other by 1.25λ.

(a) What is the phase difference between the two waves arriving at point P?

(b) Determine the intensity at P, expressed as a fraction of the maximum intensity Iₒ on the screen.

Suppose that one slit of a double-slit apparatus is wider than the other so that the intensity of light passing through it is twice as great. Determine the intensity I as a function of position (θ) on the screen for coherent light.

Design a double-slit apparatus so that the central diffraction peak contains precisely fifteen fringes. Assume the first diffraction minimum occurs at (a) an interference minimum, (b) an interference maximum.