34. Wave Optics

A diffraction grating with $500\text{lines}/\mathrm{mm}$ is illuminated by two wavelengths of light: $450\mathrm{nm}$ and $600\mathrm{nm}.$ What is the distance between the $m=2$ bright fringes of the two colors of light on a screen $1.3\mathrm{m}$ away?

A diffraction grating has $500\text{lines}/\mathrm{mm}.$ If it is illuminated by a laser at $532\mathrm{nm},$ how many bright spots will be observed on a screen placed behind the grating?

A particular kind of oil with an index of refraction of $1.46$ has spilled on water. The different thicknesses of the oil slick result in different colors being strongly reflected at different parts of the spill. But near the edges, you identify the thinnest part of the oil layer that strongly reflects green light with a wavelength of 550 nm when you are directly overhead. What is the thickness of the oil at this point? Assume light is incident normal to the oil surface.

You place one glass slide on top of another, with an animal hair between them at one end. You illuminate the slides with blue light of wavelength $450\mathrm{nm}.$ You count along the slide and find 300 transitions from bright to dark and back to light. How thick is the hair?

A carbon dioxide laser produces $10.6\mathrm{\mu }\mathrm{m}$ electromagnetic waves, which pass through a circular aperture with diameter $1.0\mathrm{mm}$. What is the approximate width of the laser beam when it strikes a target $3.0\mathrm{m}$ away?

A $480\mathrm{nm}$ light is used to illuminate a diffraction grating with $500\mathrm{lines}/\mathrm{mm}$. What is the angle, measured from the central maximum, to the m=3 bright fringe?

Light from a helium-neon laser (λ=633 nm) passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The width of the central maximum is 2.5 cm. What is the diameter (in mm) of the hole?

You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.0 cm. You have a helium-neon laser (λ=633 nm) and a 0.12-mm-diameter pinhole. How far behind the pinhole should you place the screen that's to be photographed?

Infrared light of wavelength 2.5 μm illuminates a 0.20-mm-diameter hole. What is the angle of the first dark fringe in radians? In degrees?

If the planes of a crystal are 3.50 Å (1 Å = 10-10 m = 1 Ångstrom unit) apart, (a) what wavelength of electromagnetic waves is needed so that the first strong interference maximum in the Bragg reflection occurs when the waves strike the planes at an angle of 22.0°, and in what part of the electromagnetic spectrum do these waves lie?