91Ó°ÊÓ

(a) At what angle is the first minimum for \(550-\mathrm{nm}\) light falling on a single slit of width \(1.00 \mu \mathrm{m}\) ? (b) Will there be a second minimum?

Consider a single-slit diffraction pattem for \(\lambda=589 \mathrm{nm},\) projected on a screen that is \(1.00 \mathrm{m}\) from a slit of width \(0.25 \mathrm{mm}\). How far from the center of the pattern are the centers of the first and second dark fringes?

If the separation between the first and the second minima of a single-slit diffraction pattem is \(6.0 \mathrm{mm}\), what is the distance between the screen and the slit? The light wavelength is \(500 \mathrm{nm}\) and the slit width is \(0.16 \mathrm{mm}\).

A single slit of width \(3.0 \mu \mathrm{m}\) is illuminated by a sodium yellow light of wavelength 589 nm. Find the intensity at a \(15^{\circ}\) angle to the axis in terms of the intensity of the central maximum.

The width of the central peak in a single-slit diffraction pattern is \(5.0 \mathrm{mm}\). The wavelength of the light is \(600 \mathrm{nm}\), and the screen is \(2.0 \mathrm{m}\) from the slit. (a) What is the width of the slit? (b) Determine the ratio of the intensity at \(4.5 \mathrm{mm}\) from the center of the pattern to the intensity at the center.

Two slits of width \(2 \mu \mathrm{m},\) each in an opaque material, are separated by a center-to-center distance of \(6 \mu \mathrm{m}\). A monochromatic light of wavelength \(450 \mathrm{nm}\) 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 pattem? (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, \(12 \mu \mathrm{m}\), while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength \(680 \mathrm{nm}\) 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?

A double slit produces a diffraction pattern that is a combination of single- and double-slit interference. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single-slit pattern falls on the fifth maximum of the double-slit pattern. (This will greatly reduce the intensity of the fifth maximum.)

Light of wavelength 500 nm falls normally on 50 slits that are \(2.5 \times 10^{-3} \mathrm{mm}\) wide and spaced \(5.0 \times 10^{-3} \mathrm{mm}\) apart. How many interference fringes lie in the central peak of the diffraction pattern?

A monochromatic light of wavelength 589 nm incident on a double slit with slit width \(2.5 \mu \mathrm{m}\) and unknown separation results in a diffraction pattem containing nine interference peaks inside the central maximum. Find the separation of the slits.

When a monochromatic light of wavelength 430 nm incident on a double slit of slit separation \(5 \mu \mathrm{m}\), there are 11 interference fringes in its central maximum. How many interference fringes will be in the central maximum of a light of wavelength \(632.8 \mathrm{nm}\) for the same double slit?