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Test prep for ap courses

Superposition of which of the following light waves may produce interference fringes? Select two answers.

Wave 1 = A 1 sin(2 ωt )

Wave 2 = A 2 sin(4 ωt )

Wave 3 = A 3 sin(2 ωt + θ )

Wave 4 = A 4 sin(4 ωt + θ ).

  1. Wave 1 and Wave 2
  2. Wave 2 and Wave 4
  3. Wave 3 and Wave 1
  4. Wave 4 and Wave 3

(b) and (c)

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In a double slit experiment with monochromatic light, the separation between the slits is 2 mm. If the screen is moved by 100 mm toward the slits, the distance between the central bright line and the second bright line changes by 32 μm. Calculate the wavelength of the light used for the experiment.

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In a double slit experiment, a student measures the maximum and minimum intensities when two waves with equal amplitudes are used. The student then doubles the amplitudes of the two waves and performs the measurements again. Which of the following will remain unchanged?

  1. The intensity of the bright fringe
  2. The intensity of the dark fringe
  3. The difference in the intensities of consecutive bright and dark fringes
  4. None of the above

(b)

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Draw a figure to show the resultant wave produced when two coherent waves (with equal amplitudes x ) interact in phase. What is the amplitude of the resultant wave? If the phase difference between the coherent waves is changed to 60º, what will be new amplitude?

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What will be the amplitude of the central fringe if the amplitudes of the two waves in a double slit experiment are a and 3 a ?

  1. 2 a
  2. 4 a
  3. 8 a 2
  4. 16 a 2

(b)

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If the ratio of amplitudes of the two waves in a double slit experiment is 3:4, calculate the ratio of minimum intensity (dark fringe) to maximum intensity (bright fringe).

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Section summary

  • Young’s double slit experiment gave definitive proof of the wave character of light.
  • An interference pattern is obtained by the superposition of light from two slits.
  • There is constructive interference when d sin θ = (for m = 0, 1, 1, 2, 2, …) size 12{d`"sin"θ=mλ,`m=0,`1,` - 1,`2,` - 2,` dotslow } {} , where d size 12{d} {} is the distance between the slits, θ size 12{θ} {} is the angle relative to the incident direction, and m size 12{m} {} is the order of the interference.
  • There is destructive interference when d sin θ = m + 1 2 λ (for m = 0, 1, 1, 2, 2, …) size 12{d`"sin"θ= left (m+ { {1} over {2} } right )λ,`m=0,`1,` - 1,`2,` - 2,` dotslow } {} .

Conceptual questions

Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

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Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

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Is it possible to create a situation in which there is only destructive interference? Explain.

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[link] shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

The figure shows a photo of a horizontal line of equally spaced red dots of light on a black background. The central dot is the brightest and the dots on either side of center are dimmer. The dot intensity decreases to almost zero after moving six dots to the left or right of center. If you continue to move away from the center, the dot brightness increases slightly, although it does not reach the brightness of the central dot. After moving another six dots, or twelve dots in all, to the left or right of center, there is another nearly invisible dot. If you move even farther from the center, the dot intensity again increases, but it does not reach the level of the previous local maximum. At eighteen dots from the center, there is another nearly invisible dot.
This double slit interference pattern also shows signs of single slit interference. (credit: PASCO)
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Problems&Exercises

At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

0 . 516º size 12{0 "." "516"°} {}

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Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

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What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of 30 . size 12{"30" "." 0°} {} ?

1 . 22 × 10 6 m size 12{1 "." "22" times "10" rSup { size 8{ - 6} } `m} {}

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Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of 45 . size 12{"45" "." 0°} {} .

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Calculate the wavelength of light that has its third minimum at an angle of 30 . size 12{"30" "." 0°} {} when falling on double slits separated by 3 . 00 μm size 12{3 "." "00"`"μm"} {} . Explicitly, show how you follow the steps in Problem-Solving Strategies for Wave Optics .

600 nm

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What is the wavelength of light falling on double slits separated by 2 . 00 μm size 12{2 "." "00"`"μm"} {} if the third-order maximum is at an angle of 60 . size 12{"60" "." 0°} {} ?

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At what angle is the fourth-order maximum for the situation in [link] ?

2 . 06º size 12{2 "." "06"°} {}

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What is the highest-order maximum for 400-nm light falling on double slits separated by 25 . 0 μm size 12{"25" "." 0`"μm"} {} ?

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Find the largest wavelength of light falling on double slits separated by 1 . 20 μm size 12{1 "." "20"`"μm"} {} for which there is a first-order maximum. Is this in the visible part of the spectrum?

1200 nm (not visible)

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What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

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(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

(a) 760 nm

(b) 1520 nm

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(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of 10 . size 12{"10" "." 0°} {} , at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?

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[link] shows a double slit located a distance x size 12{x} {} from a screen, with the distance from the center of the screen given by y size 12{y} {} . When the distance d size 12{d} {} between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where sin θ θ size 12{"sin"θ approx θ} {} , with θ size 12{θ} {} in radians), the distance between fringes is given by Δ y = / d size 12{Δy=xλ/d} {} .

The figure shows a schematic of a double slit experiment. A double slit is at the left and a screen is at the right. The slits are separated by a distance d. From the midpoint between the slits, a horizontal line labeled x extends to the screen. From the same point, a line angled upward at an angle theta above the horizontal also extends to the screen. The distance between where the horizontal line hits the screen and where the angled line hits the screen is marked y, and the distance between adjacent fringes is given by delta y, which equals x times lambda over d.
The distance between adjacent fringes is Δ y = / d size 12{Δy=xλ/d} {} , assuming the slit separation d size 12{d} {} is large compared with λ size 12{λ} {} .

For small angles sin θ tan θ θ ( in radians ) size 12{"sin"θ - "tan"θ approx θ` \( "in"`"radians" \) } {} .

For two adjacent fringes we have,

d sin θ m = size 12{d`"sin"θ rSub { size 8{m} } =mλ} {}

and

d sin θ m + 1 = m + 1 λ size 12{d`"sin "θ rSub { size 8{m+1} } = left (m+1 right )λ} {}

Subtracting these equations gives

d sin θ m + 1 sin θ m = m + 1 m λ d θ m + 1 θ m = λ tan θ m = y m x θ m d y m + 1 x y m x = λ d Δ y x = λ Δ y = d alignl { stack { size 12{d left ("sin"θ rSub { size 8{m+1} } - " sin"θ rSub { size 8{m} } right )= left [ left (m+1 right ) - m right ]λ} {} # d left (θ rSub { size 8{m+1} } - θ"" lSub { size 8{m} } right )=λ {} #"tan"θ rSub { size 8{m} } = { {y rSub { size 8{m} } } over {x} } approx θ"" lSub { size 8{m} } drarrow d left ( { {y rSub { size 8{m+1} } } over {x} } - { {y rSub { size 8{m} } } over {x} } right )=λ {} # d { {Δy} over {x} } =λ drarrow {underline {Δy= { {xλ} over {d} } }} {}} } {}

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Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in [link] .

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Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see [link] ).

450 nm

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
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David
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emma Reply
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Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
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can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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