What is the shape of the curve for curvature radius vs. refractive index with a constant focal length? what happens to the required index of refraction as the radius becomes arbitrarily large or arbitrarily small? what conclusions can you draw about the material requirements of manufacturing small spherical lenses for use in personal electronic devices?

The place you get your hair cut has two nearly parallel mirrors 6.00 m apart. as you sit in the chair, your head is 2.00 m from the nearer mirror. looking toward this mirror, you first see your face and then, farther away, the back of your head. (the mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) how far away does the back of your head appear to be?

Matt is driving down 7th street. he drives 150 meters in 18 sec. assuming he doesn’t slow down or speed up, what is his speed?

A175 g lump of molten lead at its melting point (327 c) is placed into 55.0 g of water at 20.0 c. the specific heat of lead is 130.j/kg c and the hf of lead is 20,400 j/kg. when the lead and the water have reached equilibrium, what is the temperature of the mixture?