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 $n_3$?