Exam 23: Light: Geometric Optics

Using monochromatic light of $410 \mathrm {~nm}$ wavelength, a single thin slit forms a diffraction pattern, with the first minimum at an angle of $40.0 ^ { \circ }$ from central maximum. The same slit, when illuminated by a new monochromatic light source, produces a diffraction pattern with the second minimum at a $60.0 ^ { \circ }$ angle from the central maximum. What is the wavelength of this new light?

The following items are positioned in sequence: A source of a beam of natural light of intensity $I _ { 0 }$ , three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, as viewed by the observer. The axis angle of polarizer $A$ is set at $0 ^ { \circ }$ (vertical), and the axis angle of polarizer $C$ is set at $50 ^ { \circ }$ . Polarizer $B$ is set so that the beam intensity is zero at the observer. What are the two possible axis angle settings (less than $180 ^ { \circ }$ ) of polarizer B?

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

When light illuminates a diffraction grating with 7000 lines per centimeter, its second order maximum is at $62.4 ^ { \circ }$ . What is the wavelength of the light?

What is the minimum thickness of a soap bubble film with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of Wavelength 610 nm?

An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating. What is the largest angle From the centerline at which an intensity maximum is formed?

What is the angular separation of two spectral lines of wavelengths $497 \mathrm {~nm}$ and $251 \mathrm {~nm}$ formed in the third order with a diffracting grating having 587 lines per millimeter?

A diffraction grating has $6.00 \times 10 ^ { 3 }$ lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength $550 \mathrm {~nm}$ ?

A beam of light of wavelength $610 \mathrm {~nm}$ passes through a slit that is $1.90 \mu \mathrm { m }$ wide. At what the angle away from the centerline does the first dark fringe occur?

A $360 - \mathrm { nm }$ thick oil film floats on the surface of a pool of water. The indices of refraction of the oil and the water are $1.50$ and $1.33$ , respectively. When the surface of the oil is illuminated from above at normal incidence with white light, what is the wavelength of light between $400 \mathrm {~nm}$ to $800 \mathrm {~nm}$ wavelength that is most weakly reflected?

Two radio antennas are $130 \mathrm {~m}$ apart on a north-south line. The two antennas radiate in phase at a frequency of $3.6 \mathrm { MHz }$ . All radio measurements are made far from the antennas. What is the smallest angle, reckoned east of north from midway between the antennas, at which constructive interference of two radio waves occurs? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A metallic sheet has a large number of parallel slits, $5.0 \mathrm {~mm}$ wide and $20 \mathrm {~cm}$ apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the intensity maxima occur $2.0 ^ { \circ }$ apart in the central region, what is the wavelength of the microwaves?

A soap bubble, when illuminated at normal incidence with light of 463 nm, appears to be especially reflective. If the index of refraction of the film is 1.35, what is the minimum thickness the soap film can be if it is surrounded by air?

Light of wavelength $687 \mathrm {~nm}$ passes through a single slit that is $0.75 \mathrm {~mm}$ wide. At what distance from the slit should a screen be placed so that the second dark fringe in the diffraction pattern is to be $1.7 \mathrm {~mm}$ from the center of the pattern?

When a light wave enters into a medium of different refractive index,

Three ideal polarizers are oriented as follows: The axis of the second polarizer is at an angle of $59.0 ^ { \circ }$ relative to the first one. The axis of the third polarizer is at an angle of $31.0 ^ { \circ }$ relative to the second one, so the axis of the axis of the third polarizer is perpendicular to the axis of the first one. Unpolarized light of intensity $18.6 \mathrm {~W} / \mathrm { m } ^ { 2 }$ is incident on the first polarizer. (a) What is the intensity of the light after it passes through all three polarizers? (b) What is the intensity of the transmitted light if the second polarizer is removed?

The following items are positioned in sequence: A source of a beam of natural light of intensity $I _ { 0 }$ , three ideal polarizers A, B, and $\mathrm { C }$ ; and an observer. Polarizer axis angles are measured clockwise from the vertical, as viewed by the observer. The axis angle of polarizer $\mathrm { A }$ is set at $0 ^ { \circ }$ (vertical), and the axis angle of polarizer $C$ is set at $50 ^ { \circ }$ . Polarizer $B$ is set so that the beam intensity at the observer is a maximum. What is the axis angle settings of polarizer B?

A diffraction grating has 450 lines per millimeter. What is the highest order $m$ that contains the entire visible spectrum from $400 \mathrm {~nm}$ to $700 \mathrm {~nm}$ ?

In a double-slit experiment, the slit separation is 1.75 mm, and two coherent wavelengths of light, 425 nm and 510 nm, illuminate the slits. At what angle from the centerline on either side of the central maximum will a bright fringe from one pattern first coincide with a bright fringe from the other pattern?

Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned. If 19% of the light passes through this combination, what is the angle between the Transmission axes of the two filters?