The index of refraction for silicate flint glass is 1.66 for violet light that has a wavelength in air equal to 400 nm and 1.61 for red light that has a wavelength in air equal to 700nm. a ray of 700-nm wavelength red light and a ray of 400-nm wavelength violet light both have angles of refraction equal to 30 degrees upon entering the glass from the air.

(a) which is greater, the angle of incidence of the ray of red light or the angle of incidence of the ray of violet light? explain your answer.

(b) what is the difference betweeen the angles of incidence of the two rays?

Aforce of 34n stretches a very light ideal spring 0.73 m from equilibrium, what is the force constant (spring constant) of the spring? (a) 47n/m (b) 38n/m (c) 53n/m (d) 25n/m

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

An incident ray through the focal point of a spherical mirror will: reflect through the center of curvature. reflect back through the focal point. reflect parallel to the principle axis. reflect the same direction as the incident ray.