Suppose reflected white light is used to observe a thin, transparent coating on glass as the coating material is gradually deposited by evaporation in a vacuum. Describe some color changes that might occur during the process of building up the thickness of the coating.

In everyday experience, why are radio waves polarized, whereas light is not?

Find numbers a, b and c such that

$$\left\{\begin{array}{l}{x=1+a t} \\ {y=2+b t} \\ {z=3+c t}\end{array}\right.$$

is perpendicular to 2x+y-3z=1.

Consider a dark fringe in an interference pattern at which almost no light energy is arriving. Light from both slits is arriving at this point, but the waves cancel. Where does the energy go?

In our discussion of thin-film interference, we looked at light reflecting from a thin film. Consider one light ray, the direct ray, that transmits through the film without reflecting. Then consider a second ray, the reflected ray, that transmits through the first surface, reflects back to the second, reflects again from the first, and then transmits out into the air, parallel to the direct ray. For normal incidence, how thick must the film be, in terms of the wavelength of the light, for the outgoing rays to interfere destructively? Is it the same thickness as for reflected destructive interference?

A lens with outer radius of curvature R and index of refraction n rests on a flat glass plate, and the combination is illuminated from white light from above. Is there a dark spot or a light spot at the center of the lens? What does it mean if the observed rings are noncircular?

Fingerprints left on a piece of glass such as a windowpane can show colored spectra like that from a diffraction grating. Why?

What ideas does the quotation from the sharecropper illuminate?

A certain oil film on water appears brightest at the outer regions, where it is thinnest. From this information, what can you say about the index of refraction of oil relative to that of water?

Why doesn't the light from the two headlights of a distant car produce an interference pattern?

Fill in each blank so that the resulting statement is true. A set that contains no elements is called the null set or the ____ set. This set is represented by { } or ____.

A simple way to observe an interference pattern is to look at a distant light source through a stretched handkerchief or an opened umbrella. Explain how that works.

Prove that the series $\sum _ { j = 0 } ^ { \infty } z ^ { j }$ does not converge uniformly to 1/(1 − z) on the opendisk |z| < 1.

A type of mirage called a pingo is often observed in Alaska. Pingos occur when the light from a small hill passes to an observer by a path that takes the light over a body of water warmer than the air. What is seen is the hill and an inverted image directly below it . Explain how these mirages are formed.