Exam 38: Diffraction Patterns and Polarization

The hydrogen spectrum has a red line at 656 nm, and a blue line at 434 nm. What is the first order angular separation between the two spectral lines obtained with a diffraction grating with 5000 rulings/cm?

The spacing between reflecting planes in a crystal is 2.82 × 10−¹⁰ m. A beam of X-rays is strongly reflected at an angle of 160° with the crystal face. What is the wavelength of the X-rays?

Polarized light is to have its polarization plane rotated by 90°. In which of the following cases does the final beam have the greatest intensity?

If the polarizing angle for cubic zirconia (zirconium oxide) is 65.6°, what is the index of refraction of the material?

Sunlight reflected from a smooth ice surface is completely polarized. Determine the angle of incidence. (n_ice = 1.31.)

When you look through a sheer curtain at a distant street lamp, you see a pattern of colored spots of light. This occurs by

Which of the patterns shown below would appear on a screen when monochromatic light first passes through a narrow slit for which a = λ and then strikes the screen? Note that the darkest area in each illustration represents the brightest area on the screen.

A diffraction grating with 4000 lines/cm is illuminated by light from the sun. The solar spectrum is spread out on a white wall across the room. At what angle from the center line does blue light (400 nm) appear? At what angle from the center line does red light (650 nm) appear?

Suppose a 5.0-meter diameter telescope were constructed on the dark side of the moon. The viewing there (except for brief periods of sunlight) would be excellent. As an example, what would be the separation between two objects that could just be resolved on the planet Mars in 500 nm light? [The distance to Mars at closest approach is 50 million miles.]

A ruby laser beam (λ = 694.3 nm) is sent outwards from a 2.7-m diameter telescope to the moon, 384,000 km away. What is the radius of the big red spot on the moon?

Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case is the slit illuminated with light of the longest wavelength?

If the interplanar spacing of NaCl is 2.814 × 10−¹⁰ m, what is the predicted angle at which X-rays of wavelength 0.140 nm will be diffracted in a first-order maximum?

Monochromatic light from a He-Ne laser (λ = 632.8 nm) is incident on a diffraction grating containing 5000 lines/cm. Determine the angle of the first-order maximum.

Light reflected off a plate-glass window (n = 1.5) is found to be completely polarized at angle-of-incidence θ. Find θ.

A single slit of width a is illuminated by light of wavelength λ. If a = 4.3λ, the maximum number of dark fringes on a semi-circular screen surrounding the slit is

When you look at a single slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the wavelength of the light is increased,

A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 × 10−⁵ radians. If λ = 5 × 10−⁷ m, what is the smallest aperture (diameter) telescope that may be used to resolve the two stars?

If the polarizing angle (the angle at which reflected light is completely plane polarized) of a flat piece of sapphire is 60.5°, what is its index of refraction?

A narrow slit is illuminated with sodium yellow light of wavelength 589 nm. If the central maximum extends to ±30.0°, how wide is the slit?

Each pattern shown below would appear on a screen when monochromatic light of wavelength λ first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case does the slit have the narrowest width?