One and Two Slit Intensity Profile Two slits are d=7w apart, where w is the width of each slit. a) What are the angles of the first three bright spots (not including the center) of the substructure (due to two-slit interference)? Express your answer in terms of A and d. b) What are the intensities of light at the angles found in the previous part (considering both the envelope due to single slit diffraction and the substructure due to two-slit interference)? Express this in terms of Io, the intensity at 0 = 0. c) Extra credit: Are any bright spots in the substructure shadowed by the envelope? If so, which ones (not necessarily found in part a)).

How far would you place a screen from the slit of the previous problem so that the second minimum is a distance of 2.5 mm from the center of the diffraction pattern?

(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

For a double-slit configuration where the slit separation is four times the slit width, how many interference fringes lie in the central peak of the diffraction pattern?

Two slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of 6 m. A monochromatic light of wavelength 450 nm is incident on the double-slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattern? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, 12 m, while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength 680 nm is used? (e) What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in (a)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?

What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

Suppose that the highest order fringe that can be observed is the eighth in a double-slit experiment where 550-nm wavelength light is used. What is the minimum separation of the slits?

As an example of diffraction by apertures of everyday dimensions, consider a doorway of width 1.0 m. (a) What is the angular position of the first minimum in the diffraction pattern of 600-nm light? (b) Repeat this calculation for a musical note of frequency 440 Hz (A above middle C). Take the speed of sound to be 343 m/s.

Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5 m in an opaque plate. A screen of dimensions 2.0m2.0m is 1.2 m away from the slit. (a) Which way is the diffraction pattern spread out on the screen? (b) What are the angles of the minima with respect to the center? (c) What are the angles of the maxima? (d) How wide is the central bright fringe on the screen? (e) How wide is the next bright fringe on the screen?

Determine the intensities of three interference peaks other than the central peak in the central maximum of the diffraction, if possible, when a light of wavelength 500 nm is incident normally on a double slit of width 1000 nm and separation 1500 nm. Use the intensity of the central spot to be 1mW/cm2 .