The light bulb in your room is not very bright. you want to use a concave mirror to direct its illumination into a tight, parallel beam of light for reading. the radius of curvature of the mirror is 30 centimeters. at what distance from the mirror should you place the light bulb to produce this parallel light beam?

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.