Question 1

A 0.72 mm diameter hole is illuminated by infrared light of wavelength 2.5 ?m. What is the angle of the first dark fringe? A) 0.24 degrees B) 4.2 × 10^-3_degrees C) 1.5 × 10^-2_degrees D) 5.6 × 10^-2_degrees

Accepted Answer

The angle of the first dark fringe is given by:sin θ = 1.22 λ/dwhere λ is the wavelength of light and d is the diameter of the hole.Plugging in the given values, we get:sin θ = 1.22 * 2.5 μm / 0.72 mmsin θ = 0.0042θ = 0.24 degrees

Question 2

The separation between adjacent maxima in a double-slit interference pattern using monochromatic light is&#10;A) greatest for red light.&#10;B) greatest for green light.&#10;C) the same for all colors of light.&#10;D) greatest for blue light.

Accepted Answer

The separation between adjacent maxima in a double-slit interference pattern is directly proportional to the wavelength of the light used. Red light has the longest wavelength among the given options, resulting in the greatest separation.

Question 3

The concentric fringes, formed when a curved lens is placed on an optical flat, are called&#10;A) Galileo circles.&#10;B) Newton's rings.&#10;C) Young's rings.&#10;D) Faraday's circles.&#10;E) Maxwell circles.

Accepted Answer

Newton's rings are formed when a curved lens is placed on an optical flat.

Question 4

After a rain, one sometimes sees brightly colored oil slicks on the road. These are due to&#10;A) interference effects.&#10;B) polarization effects.&#10;C) diffraction effects.&#10;D) selective absorption of different wavelengths by oil.&#10;E) birefringence.

Accepted Answer

The brightly colored oil slicks are due to interference effects, where light waves reflected from the top and bottom surfaces of the thin oil film interfere with each other, creating a spectrum of colors.

Question 5

We have seen that two monochromatic light waves can interfere constructively or destructively, depending on their phase difference. One consequence of this phenomena is&#10;A) the colors you see when white light is reflected from a soap bubble.&#10;B) a rainbow.&#10;C) the appearance of a mirage in the desert.&#10;D) the way in which polarized sunglasses work.&#10;E) the formation of an image by a converging lens, such as the lens in your eye.

Accepted Answer

The colors seen in a soap bubble are due to thin-film interference, where different wavelengths of light interfere constructively or destructively depending on the thickness of the film and the angle of incidence.

Question 6

In terms of the wavelength of light in soapy water, what is the minimum thickness of soap film that will reflect a given wavelength of light?&#10;A) one-fourth wavelength&#10;B) one-half wavelength&#10;C) one wavelength&#10;D) two wavelengths&#10;E) there is no minimum thickness

Accepted Answer

The minimum thickness of a soap film that will reflect a given wavelength of light is one-fourth of the wavelength. This is due to the interference of light waves reflecting off the front and back surfaces of the film, which requires a path difference of half a wavelength for constructive interference. Since the light travels through the film twice, the thickness must be one-fourth of the wavelength in the medium.

Question 7

A soap film is being viewed in white light. As the film becomes very much thinner than the wavelength of blue light, the film&#10;A) appears black because it reflects no visible light.&#10;B) appears blue since all other colors are transmitted.&#10;C) appears white because it reflects all wavelengths of visible light.&#10;D) appears red since all other colors are transmitted.

Accepted Answer

As the film becomes much thinner than the wavelength of visible light, destructive interference occurs for all visible wavelengths, causing the film to appear black.

Question 8

The condition for interference maxima for a diffraction grating is identical to that for&#10;A) a narrowing single slit.&#10;B) a double slit.&#10;C) a thin film.&#10;D) a wide single slit.

Accepted Answer

The condition for interference maxima for a diffraction grating is similar to that for a double slit, where constructive interference occurs at angles where the path difference between adjacent slits is an integer multiple of the wavelength.

Question 9

You want to confine an electron in a box so that its minimum energy is 5.0 × 10^-18 J. What is the length of the box? A) 0.11 nm B) 0.22 nm C) 0.15 nm D) 0.18 nm

Accepted Answer

The minimum energy of an electron in a box is given by:$$E_n = \frac{n^2h^2}{8mL^2}$$where:* $E_n$ is the energy of the electron in joules* $n$ is the principal quantum number* $h$ is Planck's constant* $m$ is the mass of the electron* $L$ is the length of the boxWe are given that the minimum energy of the electron is $5.0 	imes 10^{-18}$ J. We can use this to solve for the length of the box:$$5.0 	imes 10^{-18} J = \frac{(1)^2(6.626 	imes 10^{-34} J \cdot s)^2}{8(9.109 	imes 10^{-31} kg)L^2}$$$$L = 0.11 nm$$Therefore, the length of the box is 0.11 nm.

Question 10

Gamma rays are photons with very high energy. What is the wavelength of a gamma-ray photon with energy 7.7 × 10^-13 J? A) 2.6 × 10^-13 m B) 3.9 × 10^-13 m C) 3.1 × 10^-13 m D) 3.5 × 10^-13 m

Accepted Answer

The energy of a photon is given by E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Rearranging this equation, we get λ = hc/E. Plugging in the given values, we get λ = (6.626 × 10^-34 J s)(3 × 10^8 m/s)/(7.7 × 10^-13 J) = 2.6 × 10^-13 m.

Question 11

You measure the velocity of an electron to an accuracy of &#177;22.6 m/s. What is the minimum uncertainty in its position?&#10;A) 8.05 ?m&#10;B) 4.03 ?m&#10;C) 16.1 ?m&#10;D) 32.2 ?m

Accepted Answer

The answer of You measure the velocity of an electron...

Question 12

Find the energy (in eV) of an optical photon of frequency 5.15 × 10^{14 Hz.} A) 2.13 eV B) 1.30 eV C) 1.56 eV D) 2.62 eV

Accepted Answer

The answer of Find the energy (in eV) of an...

Deck 7: Wave Optics and Modern Physics