91Ó°ÊÓ

Parallel light of wavelength \(6563 \mathrm{~A}\) is incident normally on a slit \(0.3850 \mathrm{~mm}\) wide. \(\mathrm{A}\) lens with a focal length of \(50.0 \mathrm{~cm}\) is located just behind the slit bringing the diffraction pattern to focus on a white screen. Find the distance from the center of the principle maximum to (a) the first minimum and (b) the fifth minimum.

Plane waves of blue light, \(\lambda=4340 \mathrm{~A}\), fall on a single slit, then pass through a lens with a focal length of \(85,0 \mathrm{~cm}\). If the central band of the diffraction pattern on the screen has a width of \(2.450 \mathrm{~mm}\), find the width of the single slit.

Find the diameter of the Airy disk in the focal plane of a refracting telescope having an objective with a focal length of \(1.0 \mathrm{~m}\) and a diameter of \(10.0 \mathrm{~cm}\). Assume the effective wavelength is \(5.50 \times 10^{-5} \mathrm{~cm} . \quad\)

The objective of a telescope has a diameter of \(12.0 \mathrm{~cm}\). At what distance would two small green objects \(30.0 \mathrm{~cm}\) apart be barely resolved by the telescope, assuming the resolution to be limited by diffraction by the objective only? Assume \(\lambda=5.40 \times\) \(10^{-5} \mathrm{~cm}\)

A source producing underwater sound waves for submarine detection has a circular aperture \(60.0 \mathrm{~cm}\) in diameter emitting waves with a frequency of \(40.0 \mathrm{kHz}\). At some distance from this source the intensity pattem will be that of a Fraunhofer pattern from a circular aperture. (a) Find the angular spread of the central lobe pattern. (b) Find the angular spread if the frequency is changed to \(4.0 \mathrm{kHz}\). Assume the speed of the sound to be \(1.50 \mathrm{~km} / \mathrm{s}\).

A parabolic radar reflector \(6.50 \mathrm{~m}\) in diameter emits microwaves with a frequency of \(6.0 \times 10^{10} \mathrm{~Hz} .\) At some distance from this source the lobe pattern is that of Fraunhofer diffraction. Find the angular width of the central lobe if the wave velocity is \(3.0 \times 10^{10} \mathrm{~cm} / \mathrm{s}\)