In the figure (a), a beam of light in material $1$ is incident on a boundary at an angle of ${\text{θ}}_1=30°.$ The extent of refraction of the light into material $2$ depends on the index of refraction $n_2$ of material $2 .$ Figure (b) gives the angle of refraction ${\text{θ}}_2$ versus $n_2$ for a range of possible $n_2$ values. The vertical axis scale is set by ${\text{θ}}_{2\mathrm{a}}=20.0°$ and ${\text{θ}}_{2\mathrm{b}}=40.0°.$ (a) What is the index of refraction of material $1?$ (b) If the incident angle is changed to $65°$ and material $2$ has $n_2=2.4,$ then what is angle ${\text{θ}}_2?$

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

In the figure, a light initially in material $1$ refracts into material $2,$ crosses that material and is then incident at the critical angle on the interface between materials $2$ and $3.$ The indexes of refraction are $n_1=1.80, n_2=1.40$ and $n_3=1.20$
(a) What is angle $\text{θ}?$
(b) If $\text{θ}$ is increased, is there refraction of light into material $3?$

A plane electromagnetic wave with wavelength $5.0 \mathrm{m}$ travels in vacuum in the positive direction of an $x$-axis. The electric field of amplitude $215 \mathrm{V} \mathrm{m}$ oscillates parallel to the $y$-axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave?
(d) What is the amplitude of the magnetic field component?

(e) Parallel to which axis does the magnetic field oscillate?

(f) What is the time-averaged rate of energy flow in watts per square meter associated with this wave? The wave uniformly illuminates a surface of area $2.0 {\mathrm{m}}^2.$ If the surface totally absorbs the wave, what are (g) the rate at which momentum is transferred to the surface and (h) the radiation pressure on the surface?