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?

Light of wavelength 690 nm passes through two narrow slits 0.66 mm apart. The screen is 1.75 m away. A second source of unknown wavelength produces its second-order fringe 1.23 mm closer to the central maximum than the 690-nm light. What is the wavelength of the unknown light?

(II) How many slits per centimeter does a grating have if the third order occurs at an 18.0° angle for 650-nm light?

A thin film of soap (n = 1.34) coats a piece of flat glass (n = 1.52). What is the minimum film thickness if it reflects 643-nm red light most strongly when illuminated normally by white light?