34. Wave Optics

A diffraction grating produces a first-order maximum at an angle of 20.0°. What is the angle of the second-order maximum?

Spy planes fly at extremely high altitudes (25 km) to avoid interception. If their cameras are to discern features as small as 5 cm, what is the minimum aperture of the camera lens to afford this resolution? (Use λ = 580nm.)

The wavelength range of the visible spectrum is approximately 380–750 nm. White light falls at normal incidence on a diffraction grating that has 350 slits/mm. Find the angular width of the visible spectrum in the first order.

A diffraction grating has 15,000 rulings in its 1.9 cm width. Determine (a) its resolving power in first and second orders, and (b) the minimum wavelength resolution (∆λ) it can yield for λ = 410 nm.

(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?

Monochromatic light falls on a transmission diffraction grating at an angle Φ to the normal.

(a) Show that Eq. 35–13 for diffraction maxima must be replaced by d(sinΦ + sinθ) = ±mλ. m = 0, 1, 2, ...

(b) Explain the ± sign.

(c) Green light with a wavelength of 550 nm is incident at an angle of 15° to the normal on a diffraction grating with 4500 slits/cm. Find the angles at which the first-order maxima occur.

Which phenomenon is primarily responsible for the fuzzy glow, or halo, observed around a full moon on a humid night?

(a) Derive an expression for the intensity in the interference pattern for three equally spaced slits. Express in terms of δ = 2πd sin θ / λ where d is the distance between adjacent slits and assume the slit width D ≈ λ.

(b) Show that there is only one secondary maximum between principal peaks.

What is the highest spectral order that can be seen if a grating with 6800 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.

Which of the following best describes the phenomenon of $diffraction$?

What is the minimum (non-zero) thickness for the air layer between two flat glass surfaces if the glass is to appear dark when 650-nm light is incident normally? What if the glass is to appear bright?

Which of the following situations will cause diffraction of a $wave$?

Which of the following correctly describes the diffraction of $\mathrm{light}$?

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).