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Check Your Understanding Suppose the slit width in [link] is increased to 1.8 × 10 −6 m . What are the new angular positions for the first, second, and third minima? Would a fourth minimum exist?

17.8 ° , 37.7 ° , 66.4 ° ; no

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Summary

  • Diffraction can send a wave around the edges of an opening or other obstacle.
  • A single slit produces an interference pattern characterized by a broad central maximum with narrower and dimmer maxima to the sides.

Conceptual questions

As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?

The diffraction pattern becomes wider.

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Compare interference and diffraction.

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If you and a friend are on opposite sides of a hill, you can communicate with walkie-talkies but not with flashlights. Explain.

Walkie-talkies use radio waves whose wavelengths are comparable to the size of the hill and are thus able to diffract around the hill. Visible wavelengths of the flashlight travel as rays at this size scale.

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What happens to the diffraction pattern of a single slit when the entire optical apparatus is immersed in water?

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In our study of diffraction by a single slit, we assume that the length of the slit is much larger than the width. What happens to the diffraction pattern if these two dimensions were comparable?

The diffraction pattern becomes two-dimensional, with main fringes, which are now spots, running in perpendicular directions and fainter spots in intermediate directions.

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A rectangular slit is twice as wide as it is high. Is the central diffraction peak wider in the vertical direction or in the horizontal direction?

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Problems

(a) At what angle is the first minimum for 550-nm light falling on a single slit of width 1.00 μ m ? (b) Will there be a second minimum?

a. 33.4 ° ; b. no

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(a) Calculate the angle at which a 2.00 - μ m -wide slit produces its first minimum for 410-nm violet light. (b) Where is the first minimum for 700-nm red light?

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(a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of 28.0 ° ? (b) At what angle will the second minimum be?

a. 1.35 × 10 −6 m ; b. 69.9 °

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(a) What is the width of a single slit that produces its first minimum at 60.0 ° for 600-nm light? (b) Find the wavelength of light that has its first minimum at 62.0 ° .

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Find the wavelength of light that has its third minimum at an angle of 48.6 ° when it falls on a single slit of width 3.00 μ m .

750 nm

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(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 μ m . At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?

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Consider a single-slit diffraction pattern for λ = 589 nm , projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?

2.4 mm, 4.7 mm

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(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 μ m . (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.

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(a) What is the minimum width of a single slit (in multiples of λ ) that will produce a first minimum for a wavelength λ ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?

a. 1.00 λ ; b. 50.0 λ ; c. 1000 λ

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(a) If a single slit produces a first minimum at 14.5 ° , at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima).

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If the separation between the first and the second minima of a single-slit diffraction pattern is 6.0 mm, what is the distance between the screen and the slit? The light wavelength is 500 nm and the slit width is 0.16 mm.

1.92 m

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A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. Ocean waves of 20.0-m wavelength approach the opening straight on. At what angles to the incident direction are the boats inside the harbor most protected against wave action?

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An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s?

45.1 °

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Questions & Answers

Note on spherical mirrors
Shamanth Reply
what is Draic equation? with explanation
M.D Reply
what is CHEMISTRY
trpathy Reply
it's a subject
Akhter
what is a Higgs Boson please?
FRANKLINE Reply
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
M.D
bro little abit getting confuse if i am wrong than please clarify me
M.D
the law of refraction of direct current lines at the boundary between two conducting media of
BATTULA Reply
what is the black body of an ideal radiator
Areej Reply
uncertainty principles is applicable to
Areej
fermions
FRANKLINE
what is the cause of the expanding universe?
FRANKLINE
microscopic particles or gases
Areej
Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart. One explanation for dark energy is that it is a property of space.
Areej
Thanks for your contribution Areej.
FRANKLINE
no problem
Areej
what is photoelectric equation
HIMANSHU Reply
How does fringe intensity depend upon slit width in single slit diffraction?
Abhishek Reply
VOLTE
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what is Draic equation
M.D
about nuclear angular momentum
rahul Reply
what is spin
MUKESH Reply
what concepts do you need?
Sumit Reply
l want physics concepts but I have not clarify on the main concepts of physics because I have studied 10 th class in Telugu medium .so what I will do
seshu Reply
what is electro magnet
Ismail Reply
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Practice Key Terms 2

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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