Inverse Square Law Calculations

Introduction

• In physics, the inverse square law is a fundamental principle that describes how a physical quantity or force diminishes with distance from a point source. In this set of calculations, we will apply the inverse square law to solve two problems related to irradiance.

Problem 1: Power Calculation

• Given: A lamp illuminates a screen of area A at a distance r. The irradiance (E) at the screen is E₀.
• We need to calculate the power (P) of the incident beam.

Solution for Problem 1

Power Calculation:

• We can calculate the power using the formula:
• E = P / A
• Rearranging for P:
• P = E × A
• Substituting the given values:
• P = E₀ × A

Problem 2: New Irradiance Calculation

• Given: If the screen is moved to a distance of r' from the lamp, we need to find the new irradiance (E').

Solution for Problem 2

New Irradiance Calculation:

• According to the inverse square law, irradiance is inversely proportional to the square of the distance from the source:
• E ∝ 1 / r²
• When the screen is moved to a new distance r', the new irradiance E' can be calculated as:
• E' = E / (r')²
• Substituting the given values:
• E' = E₀ / (r')²

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Physics

Inverse Square Law Calculations