High School

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Light with a wavelength of 610 nm is incident on a 0.20 m wide slit, and the diffraction pattern is produced on a screen 1.5m from the slit. what is the width of the central maximum?

Answer :

The width of the central maximum in a single-slit diffraction pattern can be calculated using the formula 2*x = λ*L/a, with λ being the wavelength of light, L the distance to the screen, and a the slit width. There is an inconsistency in the question regarding the units for slit width, but converting to the correct units would allow for the calculation of the width of the central maximum.

The student has asked about the width of the central maximum in a single-slit diffraction pattern. When monochromatic light with a wavelength of 610 nm is incident on a 0.20 m wide slit, and a diffraction pattern is produced on a screen 1.5 m away. To find the central maximum's width, we can use the formula for the width of the central diffraction peak in a single-slit experiment:

2*x = λ*L/a
Where:

  • λ (lambda) is the wavelength of the light,
  • L is the distance from the slit to the screen,
  • a is the width of the slit,
  • x is the distance from the center to the first minimum on one side of the pattern (so 2*x is the total width of the central maximum).

To find the central maximum's width, one would plug the given values into the formula and solve for x. However, the values given here do not seem to match the question being asked, as there are inconsistencies in the slit width units. Assuming the slit width is 0.20 mm (instead of 0.20 m), we would convert millimeters to meters and then calculate. For instance:

x = (610e-9 m * 1.5 m) / (0.20e-3 m)

The width of the central maximum would be 2*x.

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