Optics 2

Question 1

Mathematical description of a wave

Answer 1

Both longitudonal and transverse waves are composed of individual paricles oscillating in SHM and obey v =flambda. We can define a function for y in terms of x and t by observing how the particle moves. This function is wthe wave function, which is given in a simplified from in equation sheet, but just use w=2pif, and f=1/T. Additionally, we can define wavenumber as 2pi/lambda to simplify the equation further.

Question 2

Wave equation

Answer 2

By taking the wave function, we can partially differentiate in terms of x or t. if we differentiate in terms of t, we get they velocity of the vibrating particles along the y axis. We can differentiate twice and prove that a=-w^2y which proves that their motion is simple harmonic. We can divide the second partial derivatives by each other to reach the wave equation. We can use the wave equation to see if a function can describe a wave. For this, you must remember v = w/k

Question 3

SHM

Answer 3

the definition of shm from circular motion is derivated to be a = -w^2x. Taking F=ma and F=-kx, acceleration for a spring in terms of x is a=-k/m x. So for simple harmonic motion to be met w = sqrt(k/m). Similarly for a simple pendilim a=-gsintheta. With small angle approximation and theta=x/L,

Question 4

Wave reflection

Answer 4

when a wave reaches an end it reflects and interferes with the incident wave. If the wave meets a fixed point, it tries to pull it and the wall pulls it down in response, causing the wave to flip and switch direction (opposite displacement). If it meets a ring it just reverses direction but doesnt fli as the ring doesnt provide a response reaction. We can add the wave functions to get the reulting wave function