Math Problem Statement

the numbers are still incorrect can you try it for single slit please maybe thats the issue

Solution

Sure! Let's go over the calculations for a single-slit diffraction scenario. Can you provide the details of the setup? Specifically, I need:

  1. Wavelength (λ\lambda) of the light in meters
  2. Slit width (aa) in meters
  3. Distance to the screen (LL) in meters
  4. Order of the fringe (mm) if you’re looking for a specific one
  5. Any measured fringe width for verification

For a single-slit diffraction pattern, the minima are given by:

asinθ=mλa \sin \theta = m \lambda

where m=1,2,3,m = 1, 2, 3, \dots (no central maximum).

The approximate fringe width (if small angles apply) is:

ymmλLay_m \approx \frac{m \lambda L}{a}

Let me know your values, and I’ll calculate it again! Also, do you want to compare this with the double-slit result?


Related Questions:

  1. How does single-slit diffraction differ from double-slit interference?
  2. What happens if the slit width is reduced?
  3. How does changing the wavelength affect the fringe pattern?
  4. Why do we use the small-angle approximation?
  5. What real-world applications use single-slit diffraction?

Tip:

If you’re measuring fringe distances, ensure your setup avoids parallax errors by looking straight on at the screen!

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Math Problem Analysis

Mathematical Concepts

Single-Slit Diffraction
Wave Optics
Trigonometry

Formulas

a sin(θ) = mλ
ym ≈ (mλL) / a

Theorems

Single-Slit Diffraction Equation

Suitable Grade Level

Grades 10-12