Challenge Problems
Determine what happens to the double-slit interference pattern if one of the slits is covered with a thin, transparent film whose thickness is , where is the wavelength of the incident light and n is the index of refraction of the film.
Fifty-one narrow slits are equally spaced and separated by 0.10 mm. The slits are illuminated by blue light of wavelength 400 nm. What is angular position of the twenty-fifth secondary maximum? What is its peak intensity in comparison with that of the primary maximum?
A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of refraction of 1.40.
Figure 3.14 shows two glass slides illuminated by monochromatic light incident perpendicularly. The top slide touches the bottom slide at one end and rests on a 0.100-mm-diameter hair at the other end, forming a wedge of air. (a) How far apart are the dark bands, if the slides are 7.50 cm long and 589-nm light is used? (b) Is there any difference if the slides are made from crown or flint glass? Explain.
Figure 3.14 shows two 7.50-cm-long glass slides illuminated by pure 589-nm wavelength light incident perpendicularly. The top slide touches the bottom slide at one end and rests on some debris at the other end, forming a wedge of air. How thick is the debris, if the dark bands are 1.00 mm apart?
A soap bubble is 100 nm thick and illuminated by white light incident at a angle to its surface. What wavelength and color of visible light is most constructively reflected, assuming the same index of refraction as water?
An oil slick on water is 120 nm thick and illuminated by white light incident at a angle to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?