34. Wave Optics

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?

(I) 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?

(II) 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?

(II) 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.

(II) 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?

(II) 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.

(III) 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.

(II) 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.

(II) 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.

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?

(II) A beam of electrons with kinetic energy 45 keV is shot through two narrow slits in a barrier. The slits are a distance 1.6 x 10⁻⁶ m apart. If a screen is placed 45.0 cm behind the barrier, calculate the spacing between the “bright” fringes of the interference pattern produced on the screen.

Two narrow slits 0.070 mm apart are illuminated by a very bright 488-nm light source forming an interference pattern on a screen 4.0 m away. Calculate (a) the distance between the m = 0 and m = 1 lines in the pattern and (b) the distance between the m = 100 and m = 101 lines.