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Conceptual questions

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

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Problems&Exercises

(a) At what angle is the first minimum for 550-nm light falling on a single slit of width 1 . 00 μm size 12{1 "." "00"`"μm"} {} ? (b) Will there be a second minimum?

(a) 33 . size 12{"33" "." 4°} {}

(b) No

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(a) Calculate the angle at which a 2 . 00 -μm size 12{2 "." "00""-μm"} {} -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 . size 12{"28" "." 0°} {} ? (b) At what angle will the second minimum be?

(a) 1 . 35 × 10 6 m size 12{1 "." "35" times "10" rSup { size 8{ - 6} } `m} {}

(b) 69 . size 12{"69" "." 9°} {}

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(a) What is the width of a single slit that produces its first minimum at 60 . size 12{"60" "." 0°} {} for 600-nm light? (b) Find the wavelength of light that has its first minimum at 62 . size 12{"62" "." 0°} {} .

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Find the wavelength of light that has its third minimum at an angle of 48 . size 12{"48" "." 6°} {} when it falls on a single slit of width 3 . 00 μm size 12{3 "." "00"`"μm"} {} .

750 nm

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Calculate the wavelength of light that produces its first minimum at an angle of 36 . size 12{"36" "." 9°} {} when falling on a single slit of width 1 . 00 μm size 12{1 "." "00"`"μm"} {} .

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(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7 . 50 μm size 12{7 "." "50"`"μm"} {} . At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?

(a) 9 . 04º size 12{9 "." "04"°} {}

(b) 12

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(a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20 . 0 μm size 12{"20" "." 0`"μm"} {} . (b) What slit width would place this minimum at 85 . size 12{"85" "." 0°} {} ? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics

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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 μm size 12{2 "." "00"`"μm"} {} . (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.

(a) 0 . 0150º size 12{0 "." "0150"°} {}

(b) 0.262 mm

(c) This distance is not easily measured by human eye, but under a microscope or magnifying glass it is quite easily measurable.

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(a) What is the minimum width of a single slit (in multiples of λ size 12{λ} {} ) that will produce a first minimum for a wavelength λ size 12{λ} {} ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?

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(a) If a single slit produces a first minimum at 14 . size 12{"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).

(a) 30 . size 12{"30" "." 1°} {}

(b) 48 . size 12{"48" "." 7°} {}

(c) No

(d) 1 = ( 2 ) ( 14.5º ) = 29º , θ 2 θ 1 = 30 . 05º 14 . = 15 . 56º size 12{2θ rSub { size 8{1} } = \( 2 \) \( "14" "." 5° \) ="29"°,~θ rSub { size 8{2} } - θ rSub { size 8{1} } ="30" "." "05"° - "14" "." 5"°=""15" "." "56"°} {} . Thus, 29º ( 2 ) ( 15 . 56º ) = 31 . size 12{"29"° approx \( 2 \) \( "15" "." "56"° \) ="31" "." 1°} {} .

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A double slit produces a diffraction pattern that is a combination of single and double slit interference. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern. (This will greatly reduce the intensity of the fifth maximum.)

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Integrated Concepts

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 angle to the incident direction are the boats inside the harbor most protected against wave action?

23 . size 12{"23" "." 6°} {} and 53 . size 12{"53" "." 1°} {}

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Integrated Concepts

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?

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Practice Key Terms 1

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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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