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MMLU-Pro / 9978 / A circular opening of radius 0.8mm in an opaque screen is illuminated by plane…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A circular opening of radius 0.8mm in an opaque screen is illuminated by plane waves of monochromatic light and the emergent light allowed to fall on a movable screen. As the screen is gradually brought toward the aperture, it is found that a succession of alternately light and dark spots appear at the center of the diffraction patterns. (a) If a bright spot appears for the second time when the distance from the screen to the position of the screen required for a bright spot to appear for the first time is 36.2 cm, find the wavelength of the light. (b) If a dark spot appears for the second time when the distance between the screen and the position of the screen required for a dark spot to appear for the first time is 36.2 cm, find the wavelength of the light. (c) Find at what distance from the screen to the aperture a bright spot appeared for the first time (refer to part (a)). (d) Find at what distance from the screen to the aperture a dark spot appeared for the first time (refer to part (b)).

category

physics

options

  1. Wavelength of light for bright spot: 1.25 × 10^-6 m, Wavelength of light for dark spot: 460mμ, First bright spot: 57 cm, First dark spot: 69 cm
  2. Wavelength of light for bright spot: 1.17 × 10^-6 m, Wavelength of light for dark spot: 442mμ, First bright spot: 54.7 cm, First dark spot: 72.4 cm
  3. Wavelength of light for bright spot: 1.5 × 10^-6 m, Wavelength of light for dark spot: 500mμ, First bright spot: 55 cm, First dark spot: 72 cm
  4. Wavelength of light for bright spot: 1.3 × 10^-6 m, Wavelength of light for dark spot: 450mμ, First bright spot: 56 cm, First dark spot: 70 cm
  5. Wavelength of light for bright spot: 1.4 × 10^-6 m, Wavelength of light for dark spot: 480mμ, First bright spot: 58 cm, First dark spot: 74 cm
  6. Wavelength of light for bright spot: 1.0 × 10^-6 m, Wavelength of light for dark spot: 420mμ, First bright spot: 52 cm, First dark spot: 75 cm
  7. Wavelength of light for bright spot: 1.3 × 10^-6 m, Wavelength of light for dark spot: 465mμ, First bright spot: 56.5 cm, First dark spot: 70.5 cm
  8. Wavelength of light for bright spot: 1.2 × 10^-6 m, Wavelength of light for dark spot: 440mμ, First bright spot: 54 cm, First dark spot: 73 cm
  9. Wavelength of light for bright spot: 1.1 × 10^-6 m, Wavelength of light for dark spot: 435mμ, First bright spot: 53 cm, First dark spot: 71 cm
  10. Wavelength of light for bright spot: 1.15 × 10^-6 m, Wavelength of light for dark spot: 450mμ, First bright spot: 55.5 cm, First dark spot: 71.5 cm

src

stemez-Optics

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Source and history

upstream_id / Original problem ID
9978
task_id
2f1056ed-7a6a-5c03-aacc-e2848ff38136
task_key
default--test--9978
task_revision_id
1
config / split
default / test

Official source

initial import