34. Wave Optics

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 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 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.

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?

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?