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Chapter 25: Problem 7

When Albert turns on his small desk lamp, the light falling on his book has intensity \(I_{0} .\) When this is not quite enough, he turns the small lamp off and turns on a high-intensity lamp so that the light on his book has intensity \(4 I_{0} .\) What is the intensity of light falling on the book when Albert turns both lamps on? If there is more than one possibility, give the range of intensity possibilities.

Short Answer

Expert verified
Answer: The range of light intensity on Albert's book when both lamps are on is between 3I_0 and 5I_0.

Step by step solution

01

Define the Intensity for Each Lamp Individually

The small lamp has an intensity of \(I_0\), and the high-intensity lamp has an intensity of \(4I_0\).
02

Determine the Minimum Intensity when Both Lamps are On

The minimum intensity occurs when both lamps are shining on the book from opposite directions such that their light intensities cancel each other out. In this case, the net intensity on the book will be the difference between the two intensities: \(4I_0 - I_0 = 3I_0\).
03

Determine the Maximum Intensity when Both Lamps are On

The maximum intensity occurs when both lamps are shining on the book from the same direction, such that their light intensities add up. In this case, the net intensity on the book will be the sum of the two intensities: \(4I_0 + I_0 = 5I_0\).
04

State the Range of Intensity Possibilities when Both Lamps are On

The intensity of the light falling on the book when both lamps are on can range from a minimum of \(3I_0\) to a maximum of \(5I_0\).

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