To measure the index of refraction of some small transparent chips of plastic of irregular shape, a physicist places the chips in a glass beaker full of water. She then gradually adds sucrose to the water until the chips suddenly become nearly invisible. Explain why a measurement of the index of refraction of the sucrose solution then yields the index of refraction of the chips of plastic.

If you wish to take a picture of yourself in a plane mirror, for what distance should the camera focus be set if you and the camera are $1.2 \mathrm{~m}$ from the mirror?

If the apex angle of a prism is $\phi=72^{\circ}$ (see Fig. 32-64), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $n=1.58$ ?

A ray of light strikes a plate of window glass of index of refraction $1.5$ and thickness $2.0 \mathrm{~mm}$ with an angle of incidence of $50^{\circ}$. Find the transverse displacement between the transmitted ray and the extrapolation of the incident ray.

The critical angle for total internal reflection in cubic zirconia (in air) is $27.0^{\circ}$. What is the polarizing angle for reflection from cubic zirconia?

At what angle above the horizon is the Sun when its light, reflected from a calm swimming pool, is linearly polarized?

An object is placed a distance $r$ in front of a wall, where $r$ exactly equals the radius of curvature of a certain concave mirror. At what distance from the wall should this mirror be placed so that a real image of the object is formed on the wall? What is the magnification of the image?

A small postage stamp is placed in front of a concave mirror (radius = R), such that the image distance equals the object distance. (a) In terms of R, what is the object distance? (b) What is the magnification of the mirror? (c) State whether the image is upright or inverted relative to the object. Draw a ray diagram to guide your thinking.

When unpolarized light is incident on sapphire at an angle of $60.5^{\circ}$, the reflected light is completely polarized. What is the index of refraction of sapphire?

A mirage is caused by a thin layer of hot air just above the ground, and its appearance is due to total internal reflection. When looking from far away, an observer sees a reflecting surface on the ground (which has the appearance of a water surface), coming from rays with an angle of reflection of $89.4^{\circ}$ or more. If the cooler air has an index of refraction $n=1.00026$,what is the index of refraction of the thin layer of hot air?

Use the formula derived from Snell's Law to consider total internal reflection at an interface with a material other than air. If a light pipe is made by coating a cylinder of crown glass with light flint glass, what is the critical angle for total internal reflection completely inside the crown glass? (Such coatings avoid problems with scratches on the outer surface.) Are there angles for which light in the crown glass will refract out into the flint glass but will still be totally internally reflected in the flint glass?

What is the critical angle for a ray of light to be internally reflected inside a plate of crown glass? What if this plate is immersed in water?

To determine the index of refraction of a liquid, an experimenter sends a ray of light through the liquid from below and measures the critical angle for total internal reflection at the upper surface. She finds that this angle is $56^{\circ}$. What is the index of refraction?

Suppose we release a short flash of light in the space between two parallel mirrors placed face to face. Why does this light flash not travel back and forth between the two mirrors forever?