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Chapter 35: Q. 3 (page 1016)

A 2.0-cm-tall object is $20 c m$ to the left of a lens with a focal length of $10 c m$ A second lens with a focal length of $15 c m$ is $30 c m$ to 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 is given below in step.

b. The position of the image is $20 cm$ away to 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 use ray tracing.

02

Part (a) step 2: Simplify

Consider :

$S_{1} = 20 c m f_{1} = 10 c m$

03

Part (b) step 1: Given information

We need to calculate the image position and height.

04

Part (b) step 2: Simplify

Finding $S_{1}^{'}$ for the first lens:

$\begin{array}{r} \frac{1}{S_{1}} + \frac{1}{S_{1}^{'}} & = \frac{1}{f_{1}} \\ S_{1}^{'} & = \frac{f_{1} S_{1}}{S_{1} 鈭� f_{1}} \\ S_{1}^{'} & = \frac{(10 cm) (20 cm)}{20 cm 鈭� 10 cm} \\ S_{1}^{'} & = \frac{200 cm}{10 cm} \\ S_{1}^{'} & = 20 cm \end{array}$

Magnification for first lens is :

$m_{1} = 鈭� \frac{S_{1}^{'}}{S_{1}} = 鈭� \frac{20 cm}{20 cm} = 鈭� 1$

For the second lens $S_{2}^{'}$ :

$\begin{array}{r} \frac{1}{S_{2}} + \frac{1}{S_{2}^{'}} & = \frac{1}{f_{2}} \\ S_{2}^{'} & = \frac{f_{2} S_{2}}{S_{2} 鈭� f_{2}} \\ S_{2}^{'} & = \frac{(15 cm) (10 cm)}{10 cm 鈭� 15 cm} \\ S_{2}^{'} & = \frac{150 cm}{鈭� 5 cm} \\ S_{2}^{'} & = 鈭� 30 cm \end{array}$

Magnification of the second lens is :

$m_{2} = - \frac{S'_{2}}{S_{2}} = - \frac{(- 30 c m)}{10 c m} = 3 c m$

Now, total magnification is:

$M = m_{1} 脳 m_{2} = (- 1) 脳 (3) = - 3$

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Most popular questions from this chapter

An astronomer is trying to observe two distant stars. The stars are marginally resolved when she looks at them through a filter that passes green light with a wavelength near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere.

A. Changing the filter to a different wavelength. If so, should she use a shorter or a longer wavelength?

B. Using a telescope with an objective lens of the same diameter but a different focal length. If so, should she select a shorter or a longer focal length?

C. Using a telescope with an objective lens of the same focal length but a different diameter. If so, should she select a larger or a smaller diameter?

D. Using an eyepiece with a different magnification. If so, should she select an eyepiece with more or less magnification?

The rays leaving the two-component optical system of FIGUREP $35.27$ produce two distinct images of the $1.0 c m$ -tall object. what are the position (relative to the lens), orientation, and height of each image?

A magnifier has a magnification of $5 x$ . How far from the lens should an object be held so that its image is seen at the near-point distance of $25 c m$ ? Assume that your is immediately behind the lens.

A microscope with a tube length of $180 m m$ achieves a total magnification of $800 X$ with a $40 X$ objectives and a $20 X$ eye piece. The microscope is focused for viewing with a related eye. how far is the sample from the objective lens?

A $2.0 m$ tall man is $10 m$ in front of a camera with a $15 mm$ focal length lens. How tall is his image on the detector?

See all solutions

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