$[25]$ When white light illuminates a thin film normal to the surface, it strongly reflects

both green$-$blue light $(500nm$ in air$),$ and dark$-$red light $(700nm$ in air$).$ Calculate the

minimum thickness of the film, if it has an index of refraction of $n=1\mathrm{.}35,$ and it floats

on water which has $n=1\mathrm{.}33.$

$[25]$ Water $(n=1\mathrm{.}33)$ in a shallow pan is covered with a thin film of oil that is $450nm$

thick, and has an index of refraction of $n=1\mathrm{.}45.$ What visible wavelengths will not be

present in the reflected light when the pan is illuminated with white light and viewed from

straight above?

A polarizer is a device which takes unpolarized light $($electric field vector oscillating equally

in all directions perpendicular to the propagation direction$),$ and allows electric fields to

be passed relative to a fixed direction $($e$.$g$.,$ the vertical$)$ with electric field components

$E_{\text{o}\text{b}\text{s}}=E_{0}cos.$

See the figure! Here $E_0$ is the amplitude of the randomly oriented field before the polar$-$

izing filter, $$ is the angle between the polarizer direction $($e$.$g$.,$ vertical$)$ and the observed

orientation. It implies that the polarizer blocks light that is polarized perpendicular to the

polarizer direction, since $cos(\frac{}{2})=0.$ The observed light intensity

$I_{\text{o}\text{b}\text{s}}=E_0^{2}co{s}^2=I_{0}co{s}^2.$

Light intensity is power per unit area $($watts$/$meter$-$squared$).$ After the polarizer light has

only vec$(E)$ fields aligned with the polarizer direction!

Problems:

$[25]$ What angle$($s$)$ does vertically polarized light make relative to a polarizing filter that

diminishes the intensity of the light by $25$ percent? Make a sketch!

$4$ a$)[10]$ what is the average of $co{s}^2$ for What does this imply for the light

intensity after the $($perfect$)$ polarizer?

b$)[5]$ Unpolarized light passes through a series of four polarizing filters which have their

polarizer axes rotated at $30$ degrees relative to each other. The first filter has the vertical

direction as its polarizer axis, the fourth one is oriented along the horizontal. Sketch the

situation.

c$)[10]$ The light which is horizontally polarized $($after the fourth polarizer$)$ has an intensity

of $250\frac{W}{m^2}.$ What was the intensity of the light source?