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82\. Two slits each of width 1800 nm and separated by the center-to-center distance of \(1200 \mathrm{nm}\) are illuminated by plane waves from a krypton ion laser-emitting at wavelength \(461.9 \mathrm{nm}\). Find the number of interference peaks in the central diffraction peak.

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

A diffraction grating produces a second maximum that is \(89.7 \mathrm{cm}\) from the central maximum on a screen \(2.0 \mathrm{m}\) away. If the grating has 600 lines per centimeter, what is the wavelength of the light that produces the diffraction pattern?

A grating with 4000 lines per centimeter is used to diffract light that contains all wavelengths between 400 and \(650 \mathrm{nm} .\) How wide is the first-order spectrum on a screen \(3.0 \mathrm{m}\) from the grating?

A diffraction grating with 2000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube. (a) At what angles will you find the maxima of the two first-order blue lines of wavelengths 410 and \(434 \mathrm{nm} ?\) (b) The maxima of two other first-order lines are found at \(\theta_{1}=0.097 \mathrm{rad}\) and \(\theta_{2}=0.132 \mathrm{rad} .\) What are the wavelengths of these lines?

For white light \((400 \mathrm{nm}<\lambda<700 \mathrm{nm})\) falling normally on a diffraction grating, show that the second and third-order spectra overlap no matter what the grating constant \(d\) is.

How many complete orders of the visible spectrum \((400 \mathrm{nm}<\lambda<700 \mathrm{nm})\) can be produced with a diffraction grating that contains 5000 lines per centimeter?

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

What are the angular positions of the first and second minima in a diffraction pattern produced by a slit of width \(0.20 \mathrm{mm}\) that is illuminated by \(400 \mathrm{nm}\) light? What is the angular width of the central peak?

The central diffraction peak of the double-slit interference pattern contains exactly nine fringes. What is the ratio of the slit separation to the slit width?