In the figure, a ray of light is perpendicular to the face $ab$ $(n=1.81).$ Find the largest value for the angle $\mathrm{\varphi }$, so that the ray is totally reflected at face $ac$ if the prism is immersed (a) in air and (b) in water.

Figure shows the light reflecting from two perpendicular reflecting surfaces $A$ and $B.$ Find the angle between the incoming ray $i$ and the outgoing ray $r^{\mathit{\text{'}}}.$

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 $3?$