<< Chapter < Page Chapter >> Page >

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)

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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).

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

[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)
Got questions? Get instant answers now!

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"°} {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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} {}

Got questions? Get instant answers now!

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°} {} .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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°} {} ?

Got questions? Get instant answers now!

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

2 . 06º size 12{2 "." "06"°} {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

(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

Got questions? Get instant answers now!

(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?

Got questions? Get instant answers now!

[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} } }} {}} } {}

Got questions? Get instant answers now!

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] .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
displacement in easy way.
Mubashir Reply
what is the Amount
Yasmin Reply
Of what? A bit of something
Antonio
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
What is position?
Amoah Reply
What is law of gravition
sushil Reply
what is magnetism
Sandeep Reply
what is charging by induction
Sandeep Reply
what is electric field lines
Sandeep Reply
law of gravitation
Rakesh Reply
Suppose a 0.250-kg ball is thrown at 15.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in [link] . (b) What is his angular velocity if each arm is 5.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.900 m) and the rest of his body as a uniform cylinder of radius 0.180 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center.
Varun Reply
Practice Key Terms 5

Get the best College physics for ap... course in your pocket!





Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask