Question 1

In a double slit experiment, the slit separation is constructed to be exactly 4 times the wavelength of the light passing through the slits. At what angles from the center of the pattern will the third bright fringes on both sides of the central fringe occur?
A) ±48.6°
B) ±75.0°
C) ±67.5°
D) ±36.9°
E) ±43.0°

Accepted Answer

A

Question 2

Coherent monochromatic light of wavelength 632.8 nm passes through a pair of thin parallel slits. The figure shows the central portion of the pattern of bright fringes viewed on a screen 1.40 m beyond the slits. What is the distance between the two slits? 
A) 0.0703 mm
B) 0.141 mm
C) 0.281 mm
D) 0.562 mm
E) 0.633 mm

Accepted Answer

C

Question 3

In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits simultaneously. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?
A) 1.5 mm
B) 3.0 mm
C) 4.5 mm
D) 6.0 mm
E) 9.0 mm

Accepted Answer

C

Question 4

Monochromatic laser light of frequency 5.20 × 10¹⁴ Hz is shown on a pair of thin parallel slits, and the pattern is viewed on a screen 1.20 m away. The fifth bright fringes (not counting the central fringe) occur at ±2.12 cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent liquid. When the experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central bright fringe. (c = 3.00 × 10⁸ m/s) (a) How far apart are the slits? (b) What is the index of refraction of the liquid?

Accepted Answer

The answer of Monochromatic laser light of frequency 5.20 ×...

Question 5

At most, how many bright fringes can be formed on each side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a double slit whose spacing is 1.97 × 10^-6 m? A) 1 B) 2 C) 3 D) 4 E) 5

Accepted Answer

The number of bright fringes on each side of the central bright fringe is given by the equation:$$N = \frac{aW}{\lambda}-1$$where:* N is the number of bright fringes* a is the slit spacing* W is the width of the screen* λ is the wavelength of lightIn this problem, we are given:* a = 1.97 × 10^-6 m* W = 1.00 m* λ = 625 nm = 6.25 × 10^-7 mSubstituting these values into the equation, we get:$$N = \frac{(1.97 	imes 10^{-6} 	ext{ m})(1.00 	ext{ m})}{6.25 	imes 10^{-7} 	ext{ m}}-1 = 3$$Therefore, there are 3 bright fringes on each side of the central bright fringe, for a total of 7 bright fringes.

Question 6

Light passes through a pair of very thin parallel slits. The resulting interference pattern is viewed far from the slits at various angles θ relative to the centerline coming outward from the midpoint between the slits. The central bright fringe is at θ = 0°. If the central bright fringe has intensity I0, what is the intensity of the next bright fringe on either side of it?
A) I0
B) I0/ 
C) I0/2
D) I0 cos 15°
E) I0 cos2 15°

Accepted Answer

The answer of Light passes through a pair of very...

Question 7

A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. Light waves arrive at the two slits in phase, and a fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 complete bright fringes per centimeter on the screen near the center of the pattern, what is the wavelength of the monochromatic light?
A) 550 nm
B) 600 nm
C) 650 nm
D) 700 nm
E) 750 nm

Accepted Answer

The answer of A pair of narrow slits, separated by...

Question 8

In the two-slit experiment, monochromatic light of frequency 5.00 × 1014 Hz passes through a pair of slits separated by 2.20 × 10^-5m. (c = 3.00 × 10⁸ m/s) (a) At what angle away from the central bright spot does the third bright fringe past the central bright spot occur? (b) At what angle does the second dark fringe occur?

Accepted Answer

The answer of In the two-slit experiment, monochromatic light of...

Question 9

In a two-slit experiment, the slit separation is 3.00 × 10^-5m. The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits. If the seventh bright fringe on the detector is 10.0 cm away from the central fringe, what is the wavelength of the light passing through the slits? A) 100 nm B) 204 nm C) 214 nm D) 224 nm E) 234 nm

Accepted Answer

The distance between the central fringe and the seventh bright fringe (n=7) is given by:

y = nλL/d

where y is the distance from the central fringe to the nth bright fringe, λ is the wavelength of the light, L is the distance from the slits to the detector, and d is the slit spacing.

Substituting the given values, we have:

10.0 cm = 7λ(2.00 m)/(3.00 × 10^-5 m)
λ = (10.0 cm)(3.00 × 10^-5 m)/(7 × 2.00 m) = 2.14 × 10^-7 m = 214 nm

Therefore, the wavelength of the light passing through the slits is 214 nm, which corresponds to choice C.

Question 10

In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m². What is the intensity halfway between the center of this fringe and the first dark band, assuming that the small-angle approximation is valid? A) 6.2 µW/m² B) 3.1 µW/m² C) 4.7 µW/m² D) 1.6 µW/m² E) 0.12 µW/m²

Accepted Answer

According to the small-angle approximation, the angle between the center of the central bright fringe and the first dark band is given by:

θ ≈ λ/d,

where λ is the wavelength of light and d is the distance between the two slits. The distance between the center of the central bright fringe and the first dark band is half the distance between two consecutive bright fringes, which is given by:

y ≈ λD/d,

where D is the distance between the double slit and the screen. Therefore, the intensity halfway between the center of the central bright fringe and the first dark band is:

I ≈ I0/4,

where I0 is the intensity at the center of the central bright fringe. Hence, we have:

I ≈ 6.2 µW/m  / 4 ≈ 1.55 µW/m.

Therefore, the best choice is B.

Question 11

Light of wavelength 519 nm passes through two slits. In the interference pattern on a screen 4.6 m away, adjacent bright fringes are separated by 5.2 mm in the general vicinity of the center of the pattern. What is the separation of the two slits?

Accepted Answer

The answer of Light of wavelength 519 nm passes through...

Question 12

Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The m = 5 bright fringe of the unknown wavelength overlaps the m = 4 bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?
A) 456 nm
B) 326 nm
C) 380 nm
D) 713 nm

Accepted Answer

The condition for bright fringes is given by the equation $ m \lambda = d \sin \theta $. For the two wavelengths to overlap, $ m_1 \lambda_1 = m_2 \lambda_2 $. Given $ m_1 = 5 $, $ \lambda_1 = \lambda $, $ m_2 = 4 $, and $ \lambda_2 = 570 $ nm, solving $ 5 \lambda = 4 \times 570 $ gives $ \lambda = 456 $ nm.

Question 13

Light from a 600 nm source goes through two slits 0.080 mm apart. What is the angular separation of the two first order maxima occurring on a screen 2.0 m from the slits?
A) 0.15°
B) 0.86°
C) 0.015°
D) 0.0075°
E) 1.75°

Accepted Answer

We can use the formula for the angular position of the bright fringes in a double-slit experiment: 
θ = λ / d 
where θ is the angular position, λ is the wavelength, and d is the distance between the slits. 
In this case, λ = 600 nm = 6.00 x 10^-7 m and d = 0.080 mm = 8.0 x 10^-5 m. 
Plugging in these values, we get: 
θ = (6.00 x 10^-7 m) / (8.0 x 10^-5 m) 
θ ≈ 0.075 radians 
To convert radians to degrees, we can multiply by 180/π: 
θ ≈ 4.30 degrees 
Since we're only interested in the separation between the first-order maxima, we need to divide this angle by 2: 
θ ≈ 2.15 degrees 
Finally, we need to convert this angle into an angular separation at the screen. We can use the small-angle approximation: 
tan θ ≈ θ = y / L 
where y is the distance between the central maximum and the first-order maximum, and L is the distance between the slits and the screen. 
In this case, L = 2.0 m and we want to solve for y. Rearranging the equation, we get: 
y = L tan θ 
Plugging in our values, we get: 
y = (2.0 m) tan (2.15 degrees) 
y ≈ 0.080 m 
So the angular separation between the first-order maxima is about 0.080 m / 2.0 m = 0.040 m = 0.86 degrees.

Question 14

Light of wavelength 575 nm passes through a double-slit and the third order bright fringe is seen at an angle of 6.5° away from the central fringe. What is the separation between the double slits?
A) 5.0 µm
B) 10 µm
C) 15 µm
D) 20 µm
E) 25 µm

Accepted Answer

We can use the formula d sinθ = mλ, where d is the separation between the double slits, θ is the angle of the bright fringe, m is the order of the fringe, and λ is the wavelength of light. We are given λ = 575 nm, θ = 6.5°, and m = 3. Solving for d, we get:

d = mλ / sinθ = (3)(575 nm) / sin 6.5°
d = 15.2 µm

Therefore, the separation between the double slits is approximately 15 µm. The closest choice is C, which is the correct answer.

Question 15

A double slit illuminated with light of wavelength 588 nm forms a diffraction pattern on a screen 11.0 cm away. The slit separation is 2464 nm. What is the distance between the third and fourth bright fringes away from the central fringe?
A) 23.9 cm
B) 5.96 cm
C) 5.59 cm
D) 2.63 cm

Accepted Answer

The answer of A double slit illuminated with light of...

Question 16

In a double slit experiment, if the separation between the two slits is 0.050 mm and the distance from the slits to a screen is 2.5 m, find the spacing between the first-order and second-order bright fringes when coherent light of wavelength 600 nm illuminates the slits.
A) 1.5 cm
B) 3.0 cm
C) 4.5 cm
D) 6.0 cm
E) 9.0 cm

Accepted Answer

The spacing between consecutive bright fringes is given by the formula:

d = λD/d

where d is the slit separation, λ is the wavelength of light, and D is the distance from the slits to the screen.

For the first-order bright fringe, we have:

d1 = λD/d = (600 nm)(2.5 m)/(0.050 mm) = 30 mm

For the second-order bright fringe, we have:

d2 = 2d1 = 2(30 mm) = 60 mm

The spacing between the first-order and second-order bright fringes is:

d2 - d1 = 60 mm - 30 mm = 30 mm = 3.0 cm

Therefore, the best choice is B.

Question 17

In a double-slit experiment, if the slit separation is increased, which of the following happens to the interference pattern shown on the screen?
A) The minima get closer together.
B) The maxima stay at the same position.
C) The minima and maxima stay at the same position.
D) The minima stay at the same position.
E) The maxima get further apart.

Accepted Answer

When the slit separation in a double-slit experiment is increased, the interference pattern on the screen changes such that the minima get closer together. This is because the fringe width is inversely proportional to the slit separation; as the separation increases, the fringe width decreases, causing the minima to move closer together.

Question 18

Light from a monochromatic source shines through a double slit onto a screen 5.00 m away. The slits are 0.180 mm apart. The dark bands on the screen are measured to be 1.70 cm apart. What is the wavelength of the incident light?
A) 457 nm
B) 306 nm
C) 392 nm
D) 612 nm
E) 784 nm

Accepted Answer

The answer of Light from a monochromatic source shines through...

Question 19

Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A woman is standing opposite the midpoint between the speakers and is initially 35.0 m from the midpoint. As she slowly walks parallel to the line connecting the speakers, at what angle θ (relative to the centerline coming outward from the midpoint between the speakers) will she first hear no sound?
A) 0.063°
B) 3.6°
C) 7.2°
D) 1.8°
E) 11°

Accepted Answer

The first position where the woman hears no sound is when there is a path difference of half a wavelength ($\lambda/2$) between the sound waves reaching her from the two speakers. The wavelength ($\lambda$) of the sound can be calculated using the formula $\lambda = v/f$, where $v$ is the speed of sound (344 m/s) and $f$ is the frequency (1100 Hz). This gives $\lambda = 344 / 1100 = 0.3127$ m. Therefore, $\lambda/2 = 0.1564$ m. The path difference corresponds to the difference in distances from each speaker to the woman's position, forming a right triangle with the line connecting the speakers and the line from the midpoint to the woman's position. Using the sine rule, $\sin(\theta) = \frac{\lambda/2}{d}$, where $d = 2.50$ m is the distance between the speakers. Substituting the values, $\sin(\theta) = \frac{0.1564}{2.50}$, giving $\theta = \arcsin(0.06256)$, which is approximately $3.6^\circ$.

Question 20

Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s) A) 43° B) 22° C) 68° D) 47° E) 30°

Accepted Answer

The path difference for constructive interference is given by $ d \sin \theta = m \lambda $, where $ d = 120 \, \text{m} $, $ \lambda = \frac{c}{f} = \frac{3.00 \times 10^8 \, \text{m/s}}{3.4 \times 10^6 \, \text{Hz}} \approx 88.24 \, \text{m} $, and $ m = 1 $ for the smallest angle. Solving for $ \theta $, we get $ \theta \approx 47^\circ $.

Quiz 34: Interference

In a double slit experiment, the slit separation is constructed to be exactly 4 times the wavelength of the light passing through the slits. At what angles from the center of the pattern will the third bright fringes on both sides of the central fringe occur?

Coherent monochromatic light of wavelength 632.8 nm passes through a pair of thin parallel slits. The figure shows the central portion of the pattern of bright fringes viewed on a screen 1.40 m beyond the slits. What is the distance between the two slits?

At most, how many bright fringes can be formed on each side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a double slit whose spacing is 1.97 × 10-6 m?

In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m2. What is the intensity halfway between the center of this fringe and the first dark band, assuming that the small-angle approximation is valid?

Light of wavelength 519 nm passes through two slits. In the interference pattern on a screen 4.6 m away, adjacent bright fringes are separated by 5.2 mm in the general vicinity of the center of the pattern. What is the separation of the two slits?

Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The m = 5 bright fringe of the unknown wavelength overlaps the m = 4 bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?

Light from a 600 nm source goes through two slits 0.080 mm apart. What is the angular separation of the two first order maxima occurring on a screen 2.0 m from the slits?

Light of wavelength 575 nm passes through a double-slit and the third order bright fringe is seen at an angle of 6.5° away from the central fringe. What is the separation between the double slits?

A double slit illuminated with light of wavelength 588 nm forms a diffraction pattern on a screen 11.0 cm away. The slit separation is 2464 nm. What is the distance between the third and fourth bright fringes away from the central fringe?

In a double slit experiment, if the separation between the two slits is 0.050 mm and the distance from the slits to a screen is 2.5 m, find the spacing between the first-order and second-order bright fringes when coherent light of wavelength 600 nm illuminates the slits.

In a double-slit experiment, if the slit separation is increased, which of the following happens to the interference pattern shown on the screen?

Light from a monochromatic source shines through a double slit onto a screen 5.00 m away. The slits are 0.180 mm apart. The dark bands on the screen are measured to be 1.70 cm apart. What is the wavelength of the incident light?

At most, how many bright fringes can be formed on each side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a double slit whose spacing is 1.97 × 10^-6 m?

In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m². What is the intensity halfway between the center of this fringe and the first dark band, assuming that the small-angle approximation is valid?