Question 1

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?

Accepted Answer

A

Question 2

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

Accepted Answer

The number of bright fringes formed on each side of the central bright fringe (not counting the central bright fringe) is given by

n = (Dλ)/(d)

where n is the number of bright fringes, D is the distance from the double slit to the screen, λ is the wavelength of the light, and d is the spacing of the slits.

Plugging in the given values, we get

n = (Dλ)/(d) = (1 × 625 × 10^-9 m)/(11.83 × 10^-6 m) ≈ 3

Therefore, the maximum number of bright fringes that can be formed on each side of the central bright fringe is 3.

Question 3

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

(a)0.163 mm (b)1.48

Question 4

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?

Accepted Answer

We can use the equation:

d*sin(θ) = m*λ

Where d is the separation between the double slits, θ is the angle of the fringe, m is the order of the fringe (in this case, m = 3), and λ is the wavelength of the light.

Rearranging this equation, we can solve for d:

d = m*λ/sin(θ)

Plugging in the values given in the problem:

d = 3*(575 nm)/(sin(6.5°))

d = 15 µm

Therefore, the separation between the double slits is 15 µm (option C).

Question 5

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?

Accepted Answer

The answer of Coherent monochromatic light of wavelength 632.8 nm...

Question 6

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 7

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.

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 8

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

Accepted Answer

To find the unknown wavelength, we can use the formula for the position of the bright fringes:

d sin θ = mλ

where d is the distance between the slits, θ is the angle between the line connecting the slit and the bright fringe and the line perpendicular to the screen, m is the order of the bright fringe (starting from m=0 for the central bright fringe), and λ is the wavelength of the light.

For the overlapping fringes, we have:

d sin θ = mλ_1   (for the light of 570 nm wavelength)
d sin θ = mλ_2   (for the unknown wavelength)

For the 11th bright fringe of the unknown wavelength to overlap with the 11th bright fringe of the 570 nm wavelength, we must have:

11λ_1 = 11λ_2
=> λ_2 = (λ_1 / 11) * 11 = 570 / 11 * 11 
=> λ_2 = 456 nm

Therefore, the answer is choice A) 456 nm.

Question 9

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?

Accepted Answer

The angular separation between the first order maxima can be found using the equation:
θ = λ/d
where θ is the angular separation, λ is the wavelength of light, and d is the distance between the two slits.
Plugging in the values, we get:
θ = (600 nm) / (0.080 mm) = 0.0075 radians
Converting to degrees, we get:
θ = 0.0075 radians * (180/π) = 0.43°
Since there are two first order maxima, the angular separation between them is twice the value we just calculated:
2θ = 0.86°
Therefore, the answer is B.

Question 10

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?

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 11

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?

Accepted Answer

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

Question 12

In a two-slit experiment,the slit separation is 3.00 ×  m.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?

Accepted Answer

We can use the following formula for the location of the bright fringes on the screen:
y = mλL/d
where y is the distance from the central fringe to the mth bright fringe, λ is the wavelength of the light, L is the distance from the slits to the screen, d is the slit separation, and m is the order of the bright fringe.

In this case, we are given y = 10.0 cm = 0.100 m, L = 2.00 m, d = 3.00 × 10^(-6) m, and m = 7. Solving for λ, we get:
λ = yd/(mL) = (0.100 m)(3.00 × 10^(-6) m)/(7)(2.00 m) = 2.14 × 10^(-7) m = 214 nm

Therefore, the best choice is C, with a wavelength of 214 nm.

Question 13

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?

Accepted Answer

According to the small-angle approximation, the path difference between the center of the central bright fringe and the first dark band is approximately λ/2. Therefore, the intensity halfway between the center of this fringe and the first dark band is given by I/4, where I is the intensity at the center of the central bright fringe. Thus, the intensity halfway between the center of this fringe and the first dark band is (6.2 µW/m^2)/4 = 1.55 µW/m^2. Therefore, choice B (3.1 µW/m^2) is the best answer, as it is the closest to this calculated value.

Question 14

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?

Accepted Answer

The answer of In a double-slit experiment,the slit separation is...

Question 15

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?

Accepted Answer

The answer of A pair of narrow slits,separated by 1.8...

Question 16

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?

Accepted Answer

The distance between dark bands (fringe spacing) is given by the formula: $ \Delta y = \frac{\lambda L}{d} $, where $ \Delta y $ is the fringe spacing, $ \lambda $ is the wavelength, $ L $ is the distance to the screen, and $ d $ is the slit separation. Rearranging for $ \lambda $, we have $ \lambda = \frac{\Delta y \cdot d}{L} $. Substituting the given values: $ \Delta y = 0.017 $ m, $ d = 0.00018 $ m, and $ L = 5.00 $ m, we find $ \lambda = \frac{0.017 \times 0.00018}{5.00} = 6.12 \times 10^{-7} $ m, or 612 nm.

Question 17

In the two-slit experiment,monochromatic light of frequency 5.00 × 10¹⁴ Hz passes through a pair of slits separated by 2.20 × 10^-5 m.(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 frequency...

Question 18

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

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 19

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)

Accepted Answer

The condition for constructive interference is that the path difference between the two waves from the antennas should be an integer multiple of the wavelength. Let's assume that the angle we are looking for is θ.

The path difference between the two waves arriving at a point P north of the antennas is given by:
Δx = d sinθ
where d is the distance between the antennas, and θ is the angle between the line connecting the antennas and the line connecting one of the antennas to point P.

The wavelength of the radio waves is given by:
λ = c/f = 88 m
where c is the speed of light and f is the frequency of the waves.

Constructive interference occurs when:
Δx = nλ
where n is an integer.

Substituting the values we have:
120 sinθ = n × 88
or
sinθ = n×88/120

Since we want the smallest angle, we take n = 1, which gives:
sinθ = 88/120
or
θ = sin−1(88/120) = 47° (rounded to the nearest degree) north of east.

Therefore, the correct answer is D.

Question 20

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?

Accepted Answer

The angle for bright fringes in a double slit experiment is given by the formula d*sin(θ) = m*λ, where d is the slit separation, m is the fringe order, and λ is the wavelength. For the third bright fringe (m=3) and d=4λ, sin(θ) = 3/4. Solving for θ gives θ = ±48.6°.

Quiz 35: Interference

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

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?

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?

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?

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.

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

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,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 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?

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

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?

Quiz 35: Interference

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

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?

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?

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?

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.

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

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,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 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?

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

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?

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?