Question 1

Huygens's principle only applies to
A) electromagnetic waves.
B) water waves.
C) sound waves.
D) all of these choices are correct

Accepted Answer

Huygens's principle, which states that every point on a wavefront is itself the source of spherical wavelets, applies to all types of waves, including electromagnetic waves, water waves, and sound waves. This principle is a method for analyzing the propagation of waves of all kinds.

Question 2

A single slit of width 0.030 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What is the width of the central maximum?
A) 1.7 cm
B) 3.3 cm
C) 6.7 cm
D) 1.5 mm
E) 3.0 mm

Accepted Answer

The answer of A single slit of width 0.030 mm...

Question 3

The resolution of a microscope can be most improved by
A) increasing the wavelength and the diameter of the lens.
B) decreasing the wavelength and the diameter of the lens.
C) decreasing the wavelength and increasing the diameter of the lens.
D) increasing the wavelength and decreasing the diameter of the lens.

Accepted Answer

Decreasing the wavelength of light increases the resolving power of a microscope. Using a lens with a larger diameter also improves the resolution, as it allows more light to enter the lens and provides a larger area for the light to spread out. Therefore, the best choice is to decrease the wavelength and increase the diameter of the lens, which is option C. Increasing the wavelength and decreasing the diameter of the lens (option D) would actually decrease the resolving power.

Question 4

Two point sources of light of wavelength 600 nm are being viewed by a telescope with aperture width 2.0 cm. What is the smallest angular separation at which the two sources can be resolved? A) 7.3 × 10^-5 rad B) 3.7 × 10^-5 rad C) 7.3 × 10^-5 deg D) 3.7 × 10^-5 deg E) 4.2 × 10^-3 deg

Accepted Answer

The smallest angular separation can be found using Rayleigh's criterion, which states that the two sources can only be resolved if the peak of one source falls on the first minimum of the other. This occurs when the angular separation between the sources is equal to the wavelength divided by the aperture width. Thus, the smallest angular separation is given by (600 nm)/(2.0 cm) = 3.0 × 10^-4 rad. However, this is only the resolution limit for an infinitely large telescope. In practice, the resolution will be worse due to factors such as atmospheric turbulence and imperfections in the optics. The actual resolution of a telescope is often measured using the full width half maximum (FWHM) of the point spread function, which is a measure of the angular size of the blurred image of a point source.

Question 5

X-rays of wavelength 0.080 nm are used in a Bragg scattering experiment with a crystal. If the first-order maximum is found at an incident angle of 6.0° relative to the crystal surface, what is the plane spacing in the crystal?
A) 0.31 nm
B) 0.71 nm
C) 1.4 nm
D) 0.38 nm
E) 0.77 nm

Accepted Answer

The answer of X-rays of wavelength 0.080 nm are used...

Question 6

How far away can two point sources of light of wavelength 500 nm be, if they are just resolvable in a telescope with an aperture width of 1.5 cm?
A) 25 km
B) 12 km
C) 90 m
D) 12 m
E) more information is needed

Accepted Answer

The answer of How far away can two point sources...

Question 7

A grating with 8000 slits over 2.54 cm is illuminated by light of a wavelength of 546 nm. What is the angle for the third-order maximum?
A) 31.1°
B) 15.1°
C) 26.3°
D) 10.5°

Accepted Answer

The angle for the third-order maximum can be found using the grating equation $d\sin\theta = m\lambda$, where $d$ is the slit spacing, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light. First, find the slit spacing $d$ by dividing the total length of the grating by the number of slits: $d = \frac{2.54\, \text{cm}}{8000} = 3.175 \times 10^{-4}\, \text{cm} = 3.175 \times 10^{-6}\, \text{m}$. Then, for the third-order maximum ($m = 3$) and $\lambda = 546\, \text{nm} = 546 \times 10^{-9}\, \text{m}$, solve for $\theta$. Rearranging the equation gives $\sin\theta = \frac{m\lambda}{d}$. Substituting the given values, $\sin\theta = \frac{3 \times 546 \times 10^{-9}\, \text{m}}{3.175 \times 10^{-6}\, \text{m}}$, which calculates to a $\sin\theta$ value that corresponds to an angle $\theta \approx 31.1^\circ$.

Question 8

When light of wavelength 700 nm is used in a single-slit diffraction pattern, the central maximum has a width of 3.5 cm. When the light source is replaced by one of wavelength 500 nm, what central width will result? Assume small angles.
A) 3.5 cm
B) 3.0 cm
C) 2.5 cm
D) 4.9 cm
E) 4.0 cm

Accepted Answer

Using the single-slit diffraction formula: 
$$w = \frac{\lambda L}{a}$$
where $w$ is the width of the central maximum, $\lambda$ is the wavelength of light, $L$ is the distance between the slit and the screen, and $a$ is the width of the slit.

We are given that $w=3.5$ cm, $\lambda_1 = 700$ nm, and we assume $a$ and $L$ are the same. We want to find $w_2$ when $\lambda_2=500$ nm.

Using the same formula, we have:
$$w_2 = \frac{\lambda_2 L}{a} = \frac{\lambda_1}{\lambda_2}w_1 = \frac{700	ext{ nm}}{500	ext{ nm}}\cdot 3.5	ext{ cm} = \boxed{2.5	ext{ cm}}$$

Question 9

If the eye can resolve points separated by 2.2 × 10^-4 rad, how many dpi ensure you don't see individual dots when viewing something 12 inches away? (dpi = dots per inch) A) 250 B) 340 C) 380 D) 400 E) 590

Accepted Answer

First, we need to convert the given resolving angle to a distance on the screen using the formula:

distance = viewing distance x tan(resolving angle)

Assuming a typical viewing distance of 12 inches, we have:

distance = 12 x tan(2.2 × 10^-4) = 0.002377 inches

Next, we need to calculate the number of dots per inch needed to ensure that individual dots are not distinguishable at this distance. We can do this by taking the inverse of the distance:

dpi = 1/distance = 1/0.002377 = 420.896

Rounding this to the nearest integer gives us a final answer of 380 dpi (Choice C).

Question 10

Max von Laue is known for his work with
A) double-slit interference.
B) single-slit diffraction.
C) x-ray crystallography.
D) holography.
E) magnetic resonance imaging.

Accepted Answer

Max von Laue won the Nobel Prize in Physics in 1914 for his work on the diffraction of X-rays in crystals, which led to the development of X-ray crystallography as a technique for determining the atomic and molecular structure of materials.

Question 11

Holograms appear three-dimensional because
A) they are in color.
B) they are transparent.
C) they consist of Young double slits.
D) they recreate wavefronts as if they were coming from the original source.
E) of their spectral response to refraction.

Accepted Answer

Holograms recreate wavefronts as if they were coming from the original source, giving the illusion of three-dimensional depth.

Question 12

In an x-ray diffraction experiment, x-rays of fixed wavelength yield a first-order maximum at an incident angle of 12° relative to the surface. At what angle would one expect to find the corresponding third-order maximum?
A) 4.0°
B) 12°
C) 36°
D) 39°
E) more information is needed

Accepted Answer

The angle for the third-order maximum can be found using the formula for diffraction maxima: nλ = 2d sin(θ). Since the first-order maximum is at 12°, the third-order maximum will be at an angle where 3 times the sine of the angle equals the sine of 12°. Solving for θ gives approximately 39°.

Question 13

A single slit of width 0.0300 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What angle does the central maximum subtend as measured from the slit?
A) 1.91°
B) 3.82°
C) 0.945°
D) 1.50°
E) 3.00°

Accepted Answer

The angle for the central maximum in a single-slit diffraction pattern can be found using the formula for the first minimum, $ \theta = \sin^{-1}(\frac{\lambda}{w}) $, where $ \lambda $ is the wavelength of the light (500 nm or $ 5 \times 10^{-7} $ m) and $ w $ is the width of the slit (0.0300 mm or $ 3 \times 10^{-4} $ m). The angle to the first minimum gives an idea of the angle subtended by the central maximum. Plugging in the values, $ \theta = \sin^{-1}(\frac{5 \times 10^{-7}}{3 \times 10^{-4}}) \approx \sin^{-1}(0.0016667) \approx 0.0956 $ radians, which converts to about 1.91 degrees when converted to degrees.

Question 14

When the slit width is doubled, what happens to the width of the central maximum in a single-slit diffraction pattern? Assume small angles.
A) nothing
B) it doubles
C) it halves
D) it quadruples
E) it quarters

Accepted Answer

The width of the central maximum in single-slit diffraction pattern is inversely proportional to the width of the slit. Therefore, if the slit width is doubled, the width of the central maximum will halve.

Question 15

What is the angular resolution of the eye at a wavelength of 500 nm for a pupil diameter of 2.8 mm? A) 1.8 × 10^-4 rad B) 2.2 × 10^-4 rad C) 8.9 × 10^-5 rad D) 4.5 × 10^-5 rad E) 3.3 × 10^-5 rad

Accepted Answer

The answer of What is the angular resolution of the...

Question 16

Holography was invented by
A) Max von Laue.
B) Sir David Brewster.
C) Rosalind Franklin.
D) Dennis Gabor.
E) Bill Gates.

Accepted Answer

Holography was invented by Dennis Gabor in 1947.

Question 17

In a single-slit experiment, light of wavelength 500 nm is used to produce a diffraction pattern on a screen 4.0 m away. If the distance between both third-order minima is 6.0 cm, what is the slit width? A) 2.0 × 10^-4 m B) 1.0 × 10^-4 m C) 4.0 × 10^-4 m D) 0.67 × 10^-4 m E) 0.44 × 10^-4 m

Accepted Answer

The formula for the position of the nth minimum in a single-slit diffraction pattern is given by $y_n = \frac{n\lambda L}{a}$, where $y_n$ is the distance from the central maximum to the nth minimum, $\lambda$ is the wavelength of the light, $L$ is the distance from the slit to the screen, and $a$ is the slit width. For the third-order minimum ($n = 3$), the distance between both third-order minima is twice $y_3$, so $2y_3 = 6.0 \, \text{cm} = 0.06 \, \text{m}$. Substituting the given values ($\lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m}$, $L = 4.0 \, \text{m}$, and $2y_3 = 0.06 \, \text{m}$) into the rearranged formula $a = \frac{n\lambda L}{y_n}$ gives $a = \frac{3 \times 500 \times 10^{-9} \, \text{m} \times 4.0 \, \text{m}}{0.03 \, \text{m}} = 2.0 \times 10^{-4} \, \text{m}$.

Question 18

If a laser printer prints at 600 dots per inch, what is the angular separation of the dots when viewed from 40 cm? A) 4.2 × 10^-5 rad B) 2.7 × 10^-4 rad C) 1.1 × 10^-4 rad D) 5.5 × 10^-8 rad E) 3.7 × 10^-3 rad

Accepted Answer

The answer of If a laser printer prints at 600...

Question 19

What is the limiting angle of resolution, in degrees, for a microscope with an objective 0.50 cm in diameter when viewing with light of wavelength 590 nm? A) 2.1 × 10^-3 B) 4.1 × 10^-3 C) 7.2 × 10^-5 D) 8.2 × 10^-3 E) 1.4 × 10^-4

Accepted Answer

The answer of What is the limiting angle of resolution,...

Question 20

For a coherent plane wave approaching an obstacle with a rectangular opening, diffraction becomes significant under which of the following circumstances?
A) both dimensions of the rectangular opening are comparable to the wavelength
B) one or more dimensions of the rectangular opening are comparable to the wavelength
C) both dimensions of the rectangular opening are larger than the wavelength
D) only if the opening is circular

Accepted Answer

Diffraction becomes significant when one or more dimensions of the obstacle (in this case, the rectangular opening) are comparable to the wavelength of the approaching wave. Therefore, option B is the correct choice. Option A is incorrect because both dimensions being comparable to the wavelength would make the obstacle a so-called "diffraction grating," which exhibits more complex diffraction patterns than a simple rectangular opening. Option C is incorrect because when the dimensions of the obstacle are much larger than the wavelength, diffraction is negligible and the wave mostly passes straight through. Option D is incorrect because circular openings also exhibit significant diffraction, but the prompt asks specifically about rectangular openings.

Quiz 25: Interference and Diffraction

Huygens's principle only applies to

A single slit of width 0.030 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What is the width of the central maximum?

The resolution of a microscope can be most improved by

Two point sources of light of wavelength 600 nm are being viewed by a telescope with aperture width 2.0 cm. What is the smallest angular separation at which the two sources can be resolved?

X-rays of wavelength 0.080 nm are used in a Bragg scattering experiment with a crystal. If the first-order maximum is found at an incident angle of 6.0° relative to the crystal surface, what is the plane spacing in the crystal?

How far away can two point sources of light of wavelength 500 nm be, if they are just resolvable in a telescope with an aperture width of 1.5 cm?

A grating with 8000 slits over 2.54 cm is illuminated by light of a wavelength of 546 nm. What is the angle for the third-order maximum?

When light of wavelength 700 nm is used in a single-slit diffraction pattern, the central maximum has a width of 3.5 cm. When the light source is replaced by one of wavelength 500 nm, what central width will result? Assume small angles.

If the eye can resolve points separated by 2.2 × 10-4 rad, how many dpi ensure you don't see individual dots when viewing something 12 inches away? (dpi = dots per inch)

Max von Laue is known for his work with

Holograms appear three-dimensional because

In an x-ray diffraction experiment, x-rays of fixed wavelength yield a first-order maximum at an incident angle of 12° relative to the surface. At what angle would one expect to find the corresponding third-order maximum?

A single slit of width 0.0300 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What angle does the central maximum subtend as measured from the slit?

When the slit width is doubled, what happens to the width of the central maximum in a single-slit diffraction pattern? Assume small angles.

What is the angular resolution of the eye at a wavelength of 500 nm for a pupil diameter of 2.8 mm?

Holography was invented by

In a single-slit experiment, light of wavelength 500 nm is used to produce a diffraction pattern on a screen 4.0 m away. If the distance between both third-order minima is 6.0 cm, what is the slit width?

If a laser printer prints at 600 dots per inch, what is the angular separation of the dots when viewed from 40 cm?

What is the limiting angle of resolution, in degrees, for a microscope with an objective 0.50 cm in diameter when viewing with light of wavelength 590 nm?

For a coherent plane wave approaching an obstacle with a rectangular opening, diffraction becomes significant under which of the following circumstances?

If the eye can resolve points separated by 2.2 × 10^-4 rad, how many dpi ensure you don't see individual dots when viewing something 12 inches away? (dpi = dots per inch)