Aglass is half-full of water, with a layer of vegetable oil (n 5 1.47) fl oating on top. a ray of light traveling downward through the oil is incident on the water at an angle of 71.48. determine the critical angle for the oil–water interface and decide whether the ray will penetrate into the water.

Identify the amplitude on the diagram and give the correct description. question 3 options: a because amplitude is the distance from wave crest to wave crest. b because the wavelength shows amplitude. c because amplitude is the distance between a crest (or trough) and rest. d because wavelength show amplitude. (brainiest if you get it right! ) ~kayla

Aball is thrown upward in the air, and its height above the ground after t seconds is h ( t ) = 57 t − 16 t 2 feet. find the time t when the ball will be traveling upward at 14.25 feet per second.

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