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?

Which of these statements is true? a. quarks pair with leptons to form protons and neutrons. b. quarks pair with bosons to form photons. c. quarks pair with photons to form protons and neutrons. d. quarks pair with other quarks to form protons and neutrons. e. quarks pair with electrons to form protons.

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.

Consider a production line with five stations. station 1 can produce a unit in 9 minutes. station 2 can produce a unit in 10 minutes. station 3 has two identical machines, each of which can process a unit in 12 minutes (each unit only needs to be processed on one of the two machines. station 4 can produce a unit in 5 minutes. station 5 can produce a unit in 8 minutes. which station is the bottleneck station?