BackFIGURE CP33.74 shows light of wavelength λ incident at angle ϕ on a reflection grating of spacing d. We want to find the angles θm at which constructive interference occurs. Light of wavelength 500 nm is incident at ϕ=40° on a reflection grating having 700 reflection lines/mm. Find all angles θm at which light is diffracted. Negative values of θm are interpreted as an angle left of the vertical.
How far must the mirror M1 in a Michelson interferometer be moved if 730 fringes of 589-nm light are to pass by a reference line?
Suppose the angles measured in Problem 42 were produced when the spectrometer (but not the source) was submerged in water. What then would be the wavelengths (in air)?
Light of wavelength 690 nm passes through two narrow slits 0.66 mm apart. The screen is 1.75 m away. A second source of unknown wavelength produces its second-order fringe 1.23 mm closer to the central maximum than the 690-nm light. What is the wavelength of the unknown light?
What is the thinnest film of MgF2 (n=1.39) on glass that produces a strong reflection for orange light with a wavelength of 600 nm?
The wings of a certain beetle have a series of parallel lines across them. When normally incident 520-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 56°. How far apart are the lines?
If a diffraction grating produces a third-order bright spot for red light (of wavelength 700 nm) at 65.0° from the central maximum, at what angle will the second-order bright spot be for violet light (of wavelength 400 nm)?
A 3800-slit/cm grating produces a third-order fringe at a 35.0° angle. What wavelength of light is being used?
Show that the second- and third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap?
Two rectangular pieces of plane glass are laid one upon the other on a table. A thin strip of paper is placed between them at one edge so that a very thin wedge of air is formed. The plates are illuminated at normal incidence by 546-nm light from a mercury-vapor lamp. Interference fringes are formed, with 15.0 fringes per centimeter. Find the angle of the wedge.
How many slits per centimeter must a grating have if there is to be no second-order spectrum for any visible wavelength?
(II) When a Newton’s ring apparatus (Fig. 34–18) is immersed in a liquid, the diameter of the tenth dark ring decreases from 2.92 cm to 2.54 cm. What is the refractive index of the liquid? [Hint: See Problem 37.]
A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread uniformly over the surface of crown glass of refractive index 1.52. Light of wavelength 520.0 nm falls at normal incidence onto the film from air. You want to increase the thickness of this film so that the reflected light cancels. What is the minimum thickness of TiO2 that you must add so the reflected light cancels as desired?
A wildlife photographer uses a moderate telephoto lens of focal length 135 mm and maximum aperture f/4.00 to photograph a bear that is 11.5 m away. Assume the wavelength is 550 nm. (a) What is the width of the smallest feature on the bear that this lens can resolve if it is opened to its maximum aperture? (b) If, to gain depth of field, the photographer stops the lens down to f/22.0, what would be the width of the smallest resolvable feature on the bear?