Homework help w/ youngs slit problems

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SUMMARY

The forum discussion centers on solving Young's slit problems related to diffraction patterns. The first problem involves calculating the total width of the central bright fringe given the distance between two fifth-order minima, with the correct answer being 8.673 cm. The second problem requires determining the width of a single slit illuminated with 649 nm light, where the distance between the first and second dark fringes is 10.2 cm. The participants express difficulty in arriving at the correct solutions, indicating a need for clearer problem-solving strategies.

PREREQUISITES
  • Understanding of Young's double-slit experiment
  • Knowledge of diffraction patterns and fringe spacing
  • Familiarity with the wave nature of light
  • Basic algebra for solving equations related to wave optics
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  • Study the derivation of the fringe width formula in Young's double-slit experiment
  • Learn about the principles of single-slit diffraction and its mathematical representation
  • Explore the concept of minima and maxima in diffraction patterns
  • Practice solving problems involving wavelength, distance, and fringe separation
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Students studying wave optics, physics educators, and anyone seeking to improve their problem-solving skills in diffraction and interference phenomena.

Verik
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I have a couple problems that I'm just not getting. Can someone help me out with these?


Problem 1

Homework Statement


A two-slit pattern is viewed on a screen 1.12m from the slits. If the two fifth-order minima are 78.5cm apart, what is the total width of the central bright fringe.

Attempts
I have gotten an array of answers, none of which are right.

4.677cm
8.673cm
and 3.014 cm



Problem 2

Homework Statement


A single slit is illuminated with 649nm light, and the resulting diffraction pattern is viewed on a screen 2.39m away. If the linear distance between the first and second dark fringes of the patter is 10.2cm, what is the width of the slit?

Attempts
nothing that came out right or making sense...
 
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Let's see what steps you took. There's no other way to spot your mistake.
 
the second one i feel like i just guessed on, i really didnt have much of a clue as to even where to start... give me a second and ill type up my work for the first.
 

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