Question

Q: Light is incident on a glass-air interface from the glass side (n=1.45), and researchers want to use the evanescent field on the air side (n=1.02) to excite the molecules adhered to the surface. It is desired that the evanescent field extends a distance of $ = 250 nm into the air side when using light of free-space wavelength of 488 nm. a) How close to critical angle must the incident beam be? (Give the difference A0 = 01-0c b) Considering that a beam with finite width contains rays with a spread of angles due to diffraction, how wide must the beam be so that the total angular spread is just equal to the difference in angles found in part a?