# 3.5 The michelson interferometer  (Page 5/7)

 Page 5 / 7

Repeat your calculation of the previous problem with the thin film placed on a flat glass ( $n=1.50$ ) surface.

After a minor oil spill, a think film of oil ( $n=1.40$ ) of thickness 450 nm floats on the water surface in a bay. (a) What predominant color is seen by a bird flying overhead? (b) What predominant color is seen by a seal swimming underwater?

a. green (504 nm); b. magenta (white minus green)

A microscope slide 10 cm long is separated from a glass plate at one end by a sheet of paper. As shown below, the other end of the slide is in contact with the plate. he slide is illuminated from above by light from a sodium lamp ( $\lambda =589\phantom{\rule{0.2em}{0ex}}\text{nm}$ ), and 14 fringes per centimeter are seen along the slide. What is the thickness of the piece of paper?

Suppose that the setup of the preceding problem is immersed in an unknown liquid. If 18 fringes per centimeter are now seen along the slide, what is the index of refraction of the liquid?

1.29

A thin wedge filled with air is produced when two flat glass plates are placed on top of one another and a slip of paper is inserted between them at one edge. Interference fringes are observed when monochromatic light falling vertically on the plates are seen in reflection. Is the first fringe near the edge where the plates are in contact a bright fringe or a dark fringe? Explain.

Two identical pieces of rectangular plate glass are used to measure the thickness of a hair. The glass plates are in direct contact at one edge and a single hair is placed between them hear the opposite edge. When illuminated with a sodium lamp ( $\lambda =589\phantom{\rule{0.2em}{0ex}}\text{nm}$ ), the hair is seen between the 180th and 181st dark fringes. What are the lower and upper limits on the hair’s diameter?

$52.7\phantom{\rule{0.2em}{0ex}}\mu \text{m}$ and $53.0\phantom{\rule{0.2em}{0ex}}\mu \text{m}$

Two microscope slides made of glass are illuminated by monochromatic ( $\lambda =589\phantom{\rule{0.2em}{0ex}}\text{nm}$ ) light incident perpendicularly. The top slide touches the bottom slide at one end and rests on a thin copper wire at the other end, forming a wedge of air. The diameter of the copper wire is $29.45\phantom{\rule{0.2em}{0ex}}\mu \text{m}$ . How many bright fringes are seen across these slides?

A good quality camera “lens” is actually a system of lenses, rather than a single lens, but a side effect is that a reflection from the surface of one lens can bounce around many times within the system, creating artifacts in the photograph. To counteract this problem, one of the lenses in such a system is coated with a thin layer of material ( $n=1.28$ ) on one side. The index of refraction of the lens glass is 1.68. What is the smallest thickness of the coating that reduces the reflection at 640 nm by destructive interference? (In other words, the coating’s effect is to be optimized for $\lambda =640\phantom{\rule{0.2em}{0ex}}\text{nm}$ .)

160 nm

Constructive interference is observed from directly above an oil slick for wavelengths (in air) 440 nm and 616 nm. The index of refraction of this oil is $n=1.54$ . What is the film’s minimum possible thickness?

A soap bubble is blown outdoors. What colors (indicate by wavelengths) of the reflected sunlight are seen enhanced? The soap bubble has index of refraction 1.36 and thickness 380 nm.

413 nm and 689 nm

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