Exam 16: Diffraction Patterns and Polarisation

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 shortest 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?

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 Hubble Space Telescope that has been placed into an Earth orbit has an aperture diameter of 2.40 metres.What angular resolution will this telescope achieve for visible light of wavelength $\lambda$ = 4.80 * 10-7 m?

Suppose a 5.0-metre diameter telescope were constructed on the dark side of the moon.The viewing there during the long lunar nights 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.]

How far above the horizon is the moon when its image, reflected in a calm lake, is completely polarised? (nwater = 1.33.)

A helium-neon laser ( $\lambda$ = 632.8 nm) is used to calibrate a diffraction grating.If the first-order maximum occurs at 20.5 $\degree$ , what is the line spacing, d?

How wide must a narrow slit be if the first diffraction minimum occurs at $\pm$ 12 $\degree$ with laser light of 633 nm?

Light strikes a flat water surface (n = 1.333) at the Brewster angle.Calculate the angle between the reflected and the refracted ray.

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

Unpolarised light is passed through three successive Polaroid filters, each with its transmission axis at 45.0 $\degree$ to the preceding filter.What percentage of light gets through?

The pupil of a cat's eye narrows to a slit width of 0.5 mm in daylight.What is the angular resolution of the cat's eye in daylight ( $\lambda$ = 500 nm)?

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

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

What, approximately, are the dimensions of the smallest object on Earth that the astronauts can resolve by eye at 200 km height from the space shuttle? Assume $\lambda$ = 500 nm light and a pupil diameter D = 0.50 cm.Assume eye fluid has an average n = 1.33.

Plane waves of ultrasound, f = 51.0 kHz, impinge on a flat plane with a 1.00 cm-wide slit.What is the total angular width (2 $\theta$ ) of diffracted sound waves when the speed of sound in air is 340 m/sec.

Each pattern shown below would appear on a screen when monochromatic light of wavelength $\lambda$ 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 greatest width?

Scattered light in the atmosphere is often partially polarised.The best way to determine whether or not light from a particular direction in the sky shows polarisation is to:

Potassium Iodide (chemical formula: KI) has a face-centred cubic structure (just like sodium chloride).If the distance between crystal planes is d = 0.353 nm and X-rays of wavelength $\lambda$ = 0.093 4 nm are used, what is the smallest angle $\theta$ at which a diffraction maximum may be obtained?

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