Exam 23: Light: Geometric Optics

A diffraction grating is to be used to find the wavelength of the emission spectrum of a gas. The grating spacing is not known, but light of a known wavelength of $632.8 \mathrm {~nm}$ is deflected by $43.2 ^ { \circ }$ in the second order by this grating. Light of the wavelength to be measured is deflected by $34.9 ^ { \circ }$ in the second order. What is the wavelength of the light that is to be measured?

The figure shows the resulting pattern when a single slit is illuminated by monochromatic light. The slit is $0.3 \times 10 ^ { - 3 } \mathrm {~m}$ wide and is illuminated by light of wavelength $506 \mathrm {~nm}$ . A diffraction pattern is seen on a screen $2.8 \mathrm {~m}$ from the slit. What is the linear distance on the screen between the first two diffraction minima on either side of the central diffraction maximum?

A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices Of refraction of gasoline and water are 1.40 and 1.33, respectively, what must be the minimum Thickness of the film to see a bright reflection?

Monochromatic light of wavelength $500 \mathrm {~nm}$ is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at $32 ^ { \circ }$ from the centerline, what is the distance between the slits of the grating?

In a two-slit experiment, the slit separation is $3.00 \times 10 ^ { - 5 } \mathrm {~m}$ . The interference pattern is created on a screen that is $2.00 \mathrm {~m}$ away from the slits. If the 7 th bright fringe on the screen is $10.0 \mathrm {~cm}$ away from the central fringe, what is the wavelength of the light?

A light beam having a wavelength of $470 \mathrm {~nm}$ in air is directed into glycerine at an angle of $75.0 ^ { \circ }$ with the normal in air. Glycerine has a refractive index of $1.47 . \left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$ (a) What are the frequency and wavelength of the light in the glycerine? (b) What angle does the light beam make with the normal in the glycerine?

Consider an experiment using a diffraction grating with 7000 lines/cm, a screen 2.50 m away, and a 440- nm wavelength beam of light. (a) How many side maxima will be observed on one side of the central maximum? (b) How far apart on the screen are the first-order and second-order maxima on the same side of the central maximum?

When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of $3 / 2$ , its speed

Light reflects off the surface of Lake Superior. What phase shift does it undergo?

Coherent light of wavelength 519 nm passes through two slits. In the resulting interference pattern on a screen 4.6 m away, adjacent bright fringes are 4.0 mm apart. What is the separation of the two slits?

In a two-slit experiment, monochromatic coherent light of wavelength $600 \mathrm {~nm}$ passes through a pair of slits separated by $2.20 \times 10 ^ { - 5 } \mathrm {~m}$ . At what angle away from the centerline does the second dark fringe occur?

A glass plate that is 2.5 cm long is separated from another glass plate at one end by a strand of someone's hair that is 0.010 mm in diameter. How far apart are the adjacent interference bands when viewed with light of wavelength 600 nm?

If a sheet containing a single slit is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction minimum?

The wavelength of light in a thin film is 360 nm and the wavelength of light in vacuum is 469 nm. What is the index of refraction for the film?

Light of wavelength $550 \mathrm {~nm}$ in air is found to travel at $1.96 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ in a certain liquid. ( $c$ $= 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ ) (a) What is the index of refraction of this liquid? (b) What is the frequency of the light in air?

A double-slit interference experiment is performed in the air. Later, the same apparatus is immersed in benzene (which has an index of refraction of 1.50), and the experiment is repeated. When the apparatus is in benzene, you observe that the interference fringes are

A single thin slit forms a diffraction pattern when illuminated with monochromatic light. The fourth minimum of the pattern occurs at an angle of $32.0 ^ { \circ }$ away from the central maximum. At what angle does the fifth minimum occur?

Unpolarized light of intensity $I _ { 0 }$ passed through an ideal polarizing sheet with its polarizing axis at the 12 o'clock position and then through a second ideal sheet with its polarizing axis at the 1 o'clock position. What is the intensity of the emerging light in terms of $I _ { 0 }$ ?

Two radio antennas are $120 \mathrm {~m}$ apart on a north-south line. The two antennas radiate in phase at a frequency of $5.6 \mathrm { MHz }$ . All radio measurements are made far from the antennas. What is the smallest angle, reckoned north of east from midway between the antennas, at which destructive interference of the two radio waves occurs? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum destructive interference is to occur at point P, the two beams Must travel paths that differ by