answer in lines/cm

When a grating is used with light that has a wavelength of 621 nm, a third-order maximum is formed at an angle of 18.0°. How many lines per centimeter does this grating have?

answer in nanometers

A mixture of red light (vacuum = 661 nm) and green light (vacuum = 551 nm) shines perpendicularly on a soap film (n = 1.41) that has air on either side. What is the minimum nonzero thickness of the film, so that destructive interference causes it to look red in reflected light?

answer in meters

Late one night on a highway, a car speeds by you and fades into the distance. Under these conditions the pupils of your eyes (average refractive index = 1.36) have diameters of about 7.0 mm. The taillights of this car are separated by a distance of 1.4 m and emit red light (wavelength = 660 nm in vacuum). How far away from you is this car when its taillights appear to merge into a single spot of light because of the effects of diffraction?

Light Spectrum

2) You are examining the light spectrum from a hot galactic gas. From the frequencies in the spectrum, you conclude that the gas is mostly made of hydrogen. From the relative intensities of each part of the spectrum, you deduce that for every 12 hydrogen atoms in the first excited state, there are 3 in the second excited state. In order to double check your conclusions about this gas's properties, you decide to predict how many hydrogen atoms are in the third excited state, relative to the 1st excited state (which you can then subsequently compare to measured values). Looking up in a table, you find that, a) the ground state has an energy of -13.6 eV, with a degeneracy of 1 b) the f... click for more

microstates

1) Polymers, like rubber, are made of very long molecules, usually tangled up. Another very crude model of a rubber band is that each link is either crumbled up or stretched. If it is crumbled up, its length is negligible and it is in the lowest energy state, call it E = 0. If it is stretched, then its length is L and it is in its high energy state of E = Eo. Consider a rubber band made of N links. The total length, Ltot, of the rubber band is the net displacement from the beginning of the first link to the end of the last link. (see attachment for rest of questions)