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Chapter 35: Q. 4 (page 1017)

A 2.0cm-tall object is 20cmto the left of a lens with a focal length of10cm. A second lens with a focal length of5cmis 30cmto the right of the first lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

Short Answer

Expert verified

a. The position and height of the image using ray tracing is given below in step.

b. The position of the image is 20cmaway from the first lens.

Step by step solution

01

Part (a) step 1: Given Information

We need to find the position and height of the image using ray tracing.

02

Part (a) step 2: Simplify

Consider:

f1=10cmf2=5cm

03

Part (b) step 1: Given Information

We need to calculate the image position and height.

04

Part (b) step 2:  Simplify

For first lens:

1S1+1S1'=1f11S1'=1f1-1S11S1'=110−1201S1'=120S1'=20cm→realimage

Next, finding value for magnification M1:

M1=−S1'S1−−2020=−1

For second lens:

1S2+1S2'=1f21S2'=1f2−1S21S2'=15−110S2'=10cm→realimage.

Next, we have to find the value for magnification M2:

M2=−S2'S2−−1010=−1

Finally, finding the total magnification M:

M=M1M2=−1−1=1

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Most popular questions from this chapter

The resolution of a digital camera is limited by two factors:

diffraction by the lens, a limit of any optical system, and the fact

that the sensor is divided into discrete pixels. Consider a typical

point-and-shoot camera that has a 20-mm-focal-length lens and

a sensor with 2.5@mm@wide pixels.

a. First,ass ume an ideal, diffractionless lens. At a distance of

100 m, what is the smallest distance, in cm, between two

point sources of light that the camera can barely resolve? In

answering this question, consider what has to happen on the

sensor to show two image points rather than one. You can use

s′ = f because s W f.

b. You can achieve the pixel-limited resolution of part a only if

the diffraction width of each image point is no greater than

1 pixel in diameter. For what lens diameter is the minimum

spot size equal to the width of a pixel? Use 600 nm for the

wavelength of light.

c. What is the f-number of the lens for the diameter you found in

part b? Your answer is a quite realistic value of the f-number

at which a camera transitions from being pixel limited to

being diffraction limited. For f-numbers smaller than this

(larger-diameter apertures), the resolution is limited by the

pixel size and does not change as you change the aperture. For

f-numbers larger than this (smaller-diameter apertures), the

resolution is limited by diffraction, and it gets worse as you

“stop down” to smaller apertures

A friend lends you the eyepiece of his microscope to use on your own microscope. He claims the spatial resolution of your microscope will be halved, since his eyepiece has the same diameter as yours but twice the magnification. Is his claim valid? Explain.

White light is incident onto a 30°prism at the 40°angleshown in Figure p35.41. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is 20%larger than the index of refraction of red light. At what angleϕdoes red light emerges from the rear face?

A scientist needs to focus a helium-neon laser beam (λ=633nm)to a 10-μm-diameterspot 8.0cmbehind a lens

(a) what focal-length lens should she use?

(b) what minimum diameter must the lens have?

Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you’re farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power +4.5Dand your right eye’s lens is +3.0D. a. Which lens should you use for the objective and which for the eyepiece? Explain.

b. What will be the magnification of your telescope?

c. How far apart should the two lenses be when you focus on distant objects?
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