Diffraction Problem, Calculate Slit Width

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SUMMARY

The diffraction problem involves calculating the slit width for light of wavelength 680 nm falling on a single slit, with a diffraction pattern observed on a screen 50 cm away. The distance between the first and third minima is given as 3 mm. The correct formula to use is y = m*lambda*R/a, where 'y' is the distance between minima, 'm' is the order of the minima, 'lambda' is the wavelength, 'R' is the distance to the screen, and 'a' is the slit width. The correct calculation shows that the slit width 'a' is 1.7 x 10^-4 m after accounting for the correct minima positions.

PREREQUISITES
  • Understanding of single-slit diffraction principles
  • Familiarity with the wave nature of light
  • Knowledge of the diffraction formula y = m*lambda*R/a
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of the single-slit diffraction formula
  • Learn about the significance of minima in diffraction patterns
  • Explore the effects of varying slit widths on diffraction patterns
  • Investigate experimental setups for measuring diffraction patterns
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Students in physics, particularly those studying wave optics, educators teaching diffraction concepts, and anyone involved in experimental physics related to light behavior.

TheRedDevil18
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Homework Statement



Light of wavelength 680nm falls onto a single slit. The diffraction pattern is observed on a screen 50cm away. If the distance between the first and the third minima is 3mm, calculate the slit width?


Homework Equations



sin thetha = m*lambda/a
y = m*lambda*R/a

The Attempt at a Solution



So the distance between the first position and last position of the dark band is 3mm?

I think this is wrong:

3*10^-3 = (3)(680*10^-9)(0.5)/a
a = 3.4*10^-4 m
 
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TheRedDevil18 said:

Homework Equations



sin thetha = m*lambda/a
y = m*lambda*R/a

The Attempt at a Solution



So the distance between the first position and last position of the dark band is 3mm?

I think this is wrong:

3*10^-3 = (3)(680*10^-9)(0.5)/a
a = 3.4*10^-4 m

There are a couple of issues with your attempt.

1. It looks like you have inserted an extra factor of 0.5 for no apparent reason.

2. Without the 0.5, the formula gives the spacing between the 3rd minimum and the central maximum.
However, the 3 mm given in the problem statement refers to the spacing between the 3rd minimum and the 1st minimum. So you need to bring the 1st minimum (n=1) into the picture.
 

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