Math Problem Statement
Solution
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Problem Summary:
We are working with monochromatic light (wavelength ) incident on a metal plate with either single or double slits, where the diffraction pattern is observed on a screen 51 cm away. The first two minima are observed at distances of 2.73 cm and 8.29 cm from the central maximum.
The goal is to determine the brightness of light at a distance of 7.65 cm from the central maxima, relative to the brightness of the central maxima.
Given Information:
- Wavelength
- Screen distance:
- First two minima positions:
- Distance of interest:
- Intensity formulas for single and double slits are provided:
- Single slit:
- Double slit:
- Single slit:
Steps to Solve:
-
Determine the type of slit configuration: Using the positions of the minima ( and ), we will analyze the spacing and check for consistency with either a single-slit or double-slit pattern.
-
Calculate angle for the given position :
Using the small-angle approximation (). -
Plug into the appropriate intensity formula: Once the configuration is determined (single or double slit), substitute into the respective intensity formula to find .
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Math Problem Analysis
Mathematical Concepts
Wave Optics
Diffraction
Interference
Small Angle Approximation
Formulas
I = I_0 (sin(πd sin(θ) / λ) / (πd sin(θ) / λ))^2 (single slit)
I = I_0 cos^2(πd sin(θ) / λ) (double slit)
sin(θ) ≈ tan(θ) ≈ y / L
Theorems
Diffraction and Interference Principles
Suitable Grade Level
Undergraduate Physics or Advanced High School
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