In Figure a light ray in air is incident at angle ${\mathrm{\theta }}_1$ on a block of transparent plastic with an index of refraction of $1.56 .$ The dimensions indicated are $H=2.00 \mathrm{cm}$ and $W=3.00 \mathrm{cm}.$ The light passes through the block to one of its sides and there undergoes reflection (inside the block) and possibly refraction (out into the air). This is the point of first reflection. The re-flected light then passes through the block to another of its sides - a point of second reflection. If ${\mathrm{\theta }}_1=40°,$ on which side is the point of (a) first reflection and (b) second reflection? If there is refraction at the point of $\left(\mathrm{c}\right)$ first reflection and $\left(\mathrm{d}\right)$ second reflection, give the angle of refraction; if not, answer "none." If ${\mathrm{\theta }}_1=75°,$ on which side is the point of $\left(\mathrm{e}\right)$ first reflection and (f) second reflection? If there is refraction at the point of $\left(g\right)$ first reflection and (h) second reflection, give the angle of refraction; if not, answer "none."

In figure, light from ray $A$ refracts from material $1 \left(n_1=1.50\right)$ into a thin layer of material $2 \left(n_2=1.80\right)$ crosses that layer and is then, incident at the critical angle on the interface between materials $2$ and $3 \left(n_3=1.30\right)$ $\left(a\right)$ What is the value of incident angle ${\mathrm{\theta }}_{\mathrm{A}}?$ $\left(b\right)$ If ${\mathrm{\theta }}_{\mathrm{A}}$ is decreased, does part of the light refract into material $3?$ Light from ray $B$ refracts from material $1$ into the thin layer, crosses that layer and is then, incident at the critical angle on the interface between materials $2$ and $3$. $\left(c\right)$ What is the value of incident angle ${\mathrm{\theta }}_{\mathrm{B}}?$ $\left(d\right)$ If ${\mathrm{\theta }}_{\mathrm{B}}$ is decreased, does part of the light refract into material $3?$

The intensity $l$ of light from an isotropic point source is determined as a function of distance $r$ from the source. Figure gives the intensity $l$ versus the inverse square $r^{-2}$ of that distance. The vertical axis scale is set by $I_{\mathrm{s}}=400 \mathrm{W} {\mathrm{m}}^{-2}$ and the horizontal axis scale is set by $r_{\mathrm{s}}^{-2}=8.0 {\mathrm{m}}^{-2}$. What is the power of the source?

In the figure, a light ray in water is incident at angle ${\mathrm{\theta }}_1$ on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction ${\mathrm{\theta }}_2$ versus the incident angle ${\mathrm{\theta }}_1$ is given in the figure $b$. The vertical axis scale is set by ${\mathrm{\theta }}_{2\mathrm{s}}=80°$. Without calculation, determine whether the index of refraction of $\left(a\right)$ material $1$ and $\left(b\right)$ material $2$ is greater or less than the index of water $(n=1.33) .$ What is the index of refraction of $\left(c\right)$ material $1$ and $\left(d\right)$ material $2$?

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

A certain helium-neon laser emits red light in a narrow band of wavelengths centered at $632.8 \mathrm{nm}$ and with a "wavelength width" (such as on the scale of figure of $5.00 \mathrm{pm}$) What is the corresponding "frequency width" for the emission?

In the figure, a light ray in air is incident on a flat layer of material $2$ that has an index of refraction, $n_2=1.7$. Beneath material $2$, is material $3$ with an index of refraction $n_3$. The ray is incident on the air-material $2$ interface at the Brewster angle for that interface. The ray of light refracted into material $3$ happens to be incident on the material $2$-material $3$ interface at the Brewster angle for that interface. What is the value of $n_3$?