Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 3

What is the inverse-square law? Use it to explain why an ordinary lightbulb can appear brighter than a star, even though the lightbulb emits far less light energy per second.

Short Answer

Expert verified
Answer: The inverse-square law explains that the intensity of light is inversely proportional to the square of the distance from its source. The lightbulb, although having a lower luminosity, appears brighter because it is closer to the observer compared to the star. The distance squared ratio in the inverse-square law indicates that the closer the object, the brighter it appears, which is why the lightbulb appears brighter despite emitting less light energy per second.

Step by step solution

01

Understand the Inverse-Square Law

The inverse-square law states that the intensity (I) of a quantity, such as light, is inversely proportional to the square of the distance (d) from its source. Mathematically, it can be expressed as: I ∝ 1/d^2
02

Calculate Apparent Brightness

Apparent brightness (B) is the brightness of an object as observed from Earth, which depends on the intensity (I) and the distance (d). Apparent brightness is given by: B = L / (4πd^2) where L is the luminosity, or the total amount of light emitted by the object.
03

Compare Lightbulb and Star Luminosity

The lightbulb emits less light energy per second (lower L) compared to a star. However, the distance (d) between the lightbulb and the observer on Earth is much less than the distance between the star and the observer.
04

Calculate Apparent Brightness Ratios

Let's denote the luminosity of the lightbulb and star as L_lightbulb and L_star, and their respective distances from the observer as d_lightbulb and d_star. We want to compare the apparent brightness of the lightbulb (B_lightbulb) and the star (B_star) using the following ratios: B_lightbulb/B_star = (L_lightbulb / (4πd_lightbulb^2)) / (L_star / (4πd_star^2))
05

Simplify the Ratio

By simplifying the ratio, the 4π term cancels out, and we get: B_lightbulb/B_star = (L_lightbulb * d_star^2) / (L_star * d_lightbulb^2)
06

Applying Inverse-Square Law

From the inverse-square law, we know that: I_lightbulb / I_star = d_star^2 / d_lightbulb^2 As apparent brightness is linked to intensity, we can see that the brighter object depends on the ratio of the distance squared.
07

Conclude

Since the distance between the lightbulb and the observer is much smaller than the distance between the star and the observer, the lightbulb appears brighter to the observer, even though it emits far less light energy per second. This is explained by the inverse-square law, which dictates how light intensity diminishes with distance.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which is more massive, a red main-sequence star or a blue mainsequence star? Which has the greater radius? Explain your answers.

Menkalinan (Arabic for "shoulder of the rein-holder") is an \(\mathrm{A} 2\) star in the constellation Auriga (the Charioteer). What is its spectral class? What is its spectral type? Which gives a more precise description of the spectrum of Menkalinan?

Why is the magnitude scale called a "backward" scale? What is the difference between apparent magnitude and absolute magnitude?

Sketch a Hertzsprung-Russell diagram. Indicate the regions on your diagram occupied by (a) main-sequence stars, (b) red giants, (c) supergiants, (d) white dwarfs, and (e) the Sun.

Why does it take at least six months to make a measurement of a star's parallax?
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Geometrical and Physical Optics

Read Explanation

Space Physics

Read Explanation

Fluids

Read Explanation

Nuclear Physics

Read Explanation

Astrophysics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free