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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

how does colour appear in thin films
Nwjwr Reply
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
Kimani Reply
derivation of lateral shieft
James Reply
Hi
Amjad
Hi
Amjad
hi
ALFRED
how are you?
Amjad
hi
asif
hi
Imran
I'm fine
ALFRED
total binding energy of ionic crystal at equilibrium is
All Reply
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Bishesh Reply
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
Sushant
What is motion
Izevbogie Reply
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
Radioactive substance
DHEERAJ
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
Celine Reply
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
Evan Reply
as a free falling object increases speed what is happening to the acceleration
Success Reply
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
Rafi Reply
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
Mohammed Reply
give any fix value to wave length
Rafi
40 cm into change mm
Arhaan Reply
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?
sisay Reply
why we have physics
Anil Reply
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
thanks buvanas
tahreem
is this a physics forum
Physics Reply
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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