How Is Slit Width Calculated in Single Slit Diffraction?

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SUMMARY

The slit width in a single slit diffraction experiment is calculated using the formula \( a = \frac{\lambda L}{y} \), where \( \lambda \) is the wavelength of light, \( L \) is the distance to the screen, and \( y \) is the distance from the central maximum to the first-order maximum. In this case, with a wavelength of 460 nm and a distance of 130 cm (0.13 m), the slit width \( a \) is determined to be 0.0272 mm. The calculation involves correctly converting units and applying the sine function to relate the parameters accurately.

PREREQUISITES
  • Understanding of single slit diffraction principles
  • Familiarity with trigonometric functions and their applications in physics
  • Knowledge of unit conversions, particularly between centimeters and meters
  • Basic grasp of wave properties, specifically wavelength
NEXT STEPS
  • Review the derivation of the single slit diffraction formula
  • Explore the impact of slit width on diffraction patterns
  • Learn about higher-order maxima and minima in diffraction
  • Investigate the effects of different wavelengths on diffraction outcomes
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Students studying physics, particularly those focusing on wave optics, as well as educators looking for practical examples of diffraction calculations.

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Homework Statement


A diffraction pattern is produced on a screen 130 cm from a single slit, using monochromatic light of wavelength 460 nm. The distance from the center of the central maximum to the first-order maximum is 2.20 mm. Calculate the slit width. (Hint: Assume that the first-order maximum is halfway between the first- and second-order minima.)


Homework Equations



y1 = L sin (theta) = L (wavelength / a)

The Attempt at a Solution



wavelength = 460 e -9 m
L = .13 m
y = .0022 m
so I found a

.0022 = .13 sin (theta)
sin (theta) = .0169 = (wavelength/ a)

a = .0272 mm

How anyone tell me what I am doing wrong?
 
Physics news on Phys.org
130\;cm \neq 0.13\;m

:wink:
 
oops :) my bad
 

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