A pair of closely spaced slits is illuminated with 572.0-nm light in a Young's double-slit experiment. During the experiment, one of the two slits is covered by an ultrathin diamond plate with index of refraction n = 2.417. What is the minimum thickness of the diamond plate that produces a dark fringe at the center of the viewing screen? nm

(a) What is the minimum width of a single slit (in multiples of ) that will produce a first minimum for a wavelength ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?

In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4? Figure P36.10

(a) What is the width of a single slit that produces its first minimum at 60.0° for 600-nm light? (b) Find the wavelength of light that has its first minimum at 62.0°.

Intense white light is incident on a diffraction grating that has 600. lines/mm. (a) What is the highest order in which the complete visible spectrum can be seen with this grating? (b) What is the angular separation between the violet edge (400. nm) and the red edge (700. nm) of the first-order spectrum produced by the grating?

Newtons rings, discovered by Isaac Newton, are an interference pattern of dark and bright rings formed because of the air gap of increasing thickness w between a spherical surface and an adjoining flat surface (Example 36.2). Figure P36.55 shows a Newtons rings apparatus with a plano-convex lens with radius of curvature R atop a flat glass slab, both with index of refraction nglass. In the configuration shown, the seventh bright fringe has a radius of 1.10 cm. After the air gap in the apparatus is filled with an unknown liquid, the radius of the seventh fringe decreases to 0.968 cm. What is the index of refraction of the unknown liquid? FIGURE P36.55

Consider the double-slit arrangement shown in Figure P37.60, where the slit separation is d and the distance from the slit to the screen is L. A sheet of transparent plastic having an index of refraction n and thickness t is placed over the upper slit. As a result, the central maximum of the interference pattern moves upward a distance y Find y.

A student sets up a double-slit experiment using mono chromatic light of wavelength . The distance between the slits is equal to 25 . (a) Find the angles at which the m = 1, 2, and 3 maxima occur on the viewing screen. (b) At what angles do the first three dark fringes occur? (c) Why are the answers so evenly spaced? Is the spacing even for all orders? Explain.

A student sets up a double-slit experiment using mono chromatic light of wavelength . The distance between the slits is equal to 25 . (a) Find the angles at which the m = 1, 2, and 3 maxima occur on the viewing screen. (b) At what angles do the first three dark fringes occur? (c) Why are the answers so evenly spaced? Is the spacing even for all orders? Explain.

Intense white light is incident on a diffraction grating that has 600. lines/mm. (a) What is the highest order in which the complete visible spectrum can be seen with this grating? (b) What is the angular separation between the violet edge (400. nm) and the red edge (700. nm) of the first-order spectrum produced by the grating?