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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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Most popular questions from this chapter

White light containing wavelengths from \(400 \mathrm{nm}\) to \(700 \mathrm{nm}\) is shone through a grating. Assuming that at least part of the third-order spectrum is present, show that the second-and third-order spectra always overlap, regardless of the slit separation of the grating.
A soap film has an index of refraction \(n=1.50 .\) The film is viewed in transmitted light. (a) At a spot where the film thickness is $910.0 \mathrm{nm},$ which wavelengths are weakest in the transmitted light? (b) Which wavelengths are strongest in transmitted light?
In a double-slit experiment, what is the linear distance on the screen between adjacent maxima if the wavelength is \(546 \mathrm{nm}\), the slit separation is \(0.100 \mathrm{mm},\) and the slit-screen separation is \(20.0 \mathrm{cm} ?\)
Show that the interference fringes in a double-slit experiment are equally spaced on a distant screen near the center of the interference pattern. [Hint: Use the small angle approximation for \(\boldsymbol{\theta} .]\)
Two radio towers are a distance \(d\) apart as shown in the overhead view. Each antenna by itself would radiate equally in all directions in a horizontal plane. The radio waves have the same frequency and start out in phase. A detector is moved in a circle around the towers at a distance of $100 \mathrm{km}.$ The waves have frequency \(3.0 \mathrm{MHz}\) and the distance between antennas is \(d=0.30 \mathrm{km} .\) (a) What is the difference in the path lengths traveled by the waves that arrive at the detector at \(\theta=0^{\circ} ?\) (b) What is the difference in the path lengths traveled by the waves that arrive at the detector at \(\theta=90^{\circ} ?\) (c) At how many angles $\left(0 \leq \theta<360^{\circ}\right)$ would you expect to detect a maximum intensity? Explain. (d) Find the angles \((\theta)\) of the maxima in the first quadrant \(\left(0 \leq \theta \leq 90^{\circ}\right) .\) (e) Which (if any) of your answers to parts (a) to (d) would change if the detector were instead only $1 \mathrm{km}$ from the towers? Explain. (Don't calculate new values for the answers.)
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