Diffraction of Light through Single Slit

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SUMMARY

The discussion focuses on calculating the wavelength (λ) of monochromatic light passing through a single slit of width 3.00 x 10-6 m, with the angle between the first dark fringes being 25 degrees. The correct application of the formula sin(θ) = nλ/w is emphasized, where θ is the angle from the central maximum. The user initially calculated λ as 1.3 x 10-6 m, but the correct wavelength is determined to be 6.49 x 10-7 m, highlighting the importance of accurately interpreting the angle in the context of the equation.

PREREQUISITES
  • Understanding of wave optics principles
  • Familiarity with the single-slit diffraction equation
  • Knowledge of trigonometric functions in physics
  • Ability to manipulate equations involving wavelength and slit width
NEXT STEPS
  • Study the derivation of the single-slit diffraction formula
  • Learn about the effects of slit width on diffraction patterns
  • Explore the concept of dark fringes and their significance in wave optics
  • Investigate the relationship between wavelength and angle in diffraction experiments
USEFUL FOR

Students studying wave optics, physics educators, and anyone interested in understanding the principles of light diffraction and its mathematical applications.

samdiah
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Homework Statement



Monochromatic light falls into slit 3.00*10^-6 wide. The angle between the first dark fringes on either side of the cental maximum is 25 derees. Calculate the λ.

w=3.00*10^-6 m
ө=25˚

Homework Equations



sin(ө) = nλ/w
sin(ө) = ((m+0.5)λ)/w
Δy=λL/w

The Attempt at a Solution



sinө=λ/w
λ=sin25*3.0*10^-6
=1.3*10^-6 m

hoever the answer is 6.49*10^-7
 
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Please help its really easy I just don't get the concept!
 
samdiah said:
The angle between the first dark fringes on either side of the cental maximum is 25 derees.
You have misinterpreted the angle. You are given the angle between the first dark fringes, but in the equation sin(theta) = n lambda/w, theta is the angle of the dark fringes measured from the central maximum.
 

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