Assume a beam of light hits the boundary separating medium 1, with index of refraction n1 and medium 2, with index of refraction n2. If total internal reflection occurs at the boundary that separates medium 1 and medium 2, then we know which of the following? a) n1= n2 b) n1< n2 c) n1> n2 d) n1 ≥ n2

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

Isla’s change in velocity is 30 m/s, and hazel has the same change in velocity. which best explains why they would have different accelerations? isla had negative acceleration, and hazel had positive. isla had a different time than hazel. isla had positive acceleration, and hazel had negative. isla went a farther distance than hazel.

You charge a parallel-plate capacitor, remove it from the battery, and prevent the wires connected to the plates from touching each other. when you increase the plate separation, what happens to the following quantities?