BackHelium atoms emit light at several wavelengths. Light from a helium lamp illuminates a diffraction grating and is observed on a screen 50.00 cm behind the grating. The emission at wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum. What is the wavelength of the bright fringe that is 31.60 cm from the central maximum?
White light (400–700 nm) incident on a 600 lines/mm diffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen 2.0 m behind the grating?
A diffraction grating has slit spacing d. Fringes are viewed on a screen at distance L. Find an expression for the wavelength of light that produces a first-order fringe on the viewing screen at distance L from the center of the screen.
A Michelson interferometer operating at a 600 nm wavelength has a 2.00-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M₂ is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00 atm pressure is 1.00028. How many bright-dark-bright fringe shifts are observed as the cell fills with air?
What is the f-number of a relaxed eye with the pupil fully dilated to 8.0 mm? Model the eye as a single lens 2.4 cm in front of the retina.
A radio telescope, whose two antennas are separated by 55 m, is designed to receive 3.0-MHz radio waves produced by astronomical objects. The received radio waves create 3.0-MHz electronic signals in the telescope’s left and right antennas. These signals then travel by equal-length cables to a centrally located amplifier, where they are added together. The telescope can be “pointed” to a certain region of the sky by adding the instantaneous signal from the right antenna to a “time-delayed” signal received by the left antenna a time ∆t ago. (This time delay of the left signal can be easily accomplished with the proper electronic circuit.) If a radio astronomer wishes to “view” radio signals arriving from an object oriented at a 12° angle to the vertical as in Fig. 34–54, what time delay ∆t is necessary?
(II) White light passes through a 640-slit/ mm diffraction grating. First-order and second-order visible spectra (“rainbows”) appear on the wall 32 cm away as shown in Fig. 35–40. Determine the widths ℓ₁ and ℓ₂ of the two “rainbows” (400 nm to 700 nm). In which order is the “rainbow” dispersed over a larger distance?
(II) X-rays of wavelength 0.138 nm fall on a crystal whose atoms, lying in planes, are spaced 0.315 nm apart. At what angle Φ (relative to the surface, Fig. 35–28) must the X-rays be directed if the first diffraction maximum is to be observed?
(II) Suppose a thin piece of glass is placed in front of the lower slit in Fig. 34–7 so that the two waves enter the slits 180° out of phase (Fig. 34–44). Describe in detail the interference pattern on the screen.
Show that the radius r of the mᵗʰ dark Newton’s ring, as viewed from directly above (Fig. 34–18), is given by r = √mλR where R is the radius of curvature of the curved glass surface and λ is the wavelength of light used. Assume that the thickness of the air gap is much less than R at all points and that r ≪ R . [Hint: Use the binomial expansion.]
(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.]
Consider two antennas radiating 6.8-MHz radio waves in phase with each other. They are located at points S₁ and S₂, separated by a distance d = 175 m, Fig. 34–50. Determine the points on the positive y-axis where the signals from the two sources will be out of phase (crests of one meet troughs of the other).
"Two identical sources S₁ and S₂, separated by distance d, coherently emit light of wavelength λ uniformly in all directions. Defining the x axis with its origin at S₁ as shown in Fig. 34–52, find the locations (expressed as multiples of λ ) where the signals from the two sources are out of phase along this axis for x > 0 , if d = 3λ.
If you can read the bottom row of your doctor’s eye chart, your eye has a resolving power of 1 arcminute, equal to 1/60 degree. If this resolving power is diffraction-limited, to what effective diameter of your eye’s optical system does this correspond? Use Rayleigh’s criterion and assume λ = 550 nm.
The VLBA (Very Long Baseline Array) uses a number of individual radio telescopes to make one unit having an equivalent diameter of about 8000 km. When this radio telescope is focusing radio waves of wavelength 2.0 cm, what would have to be the diameter of the mirror of a visible-light telescope focusing light of wavelength 550 nm so that the visible-light telescope has the same resolution as the radio telescope?