Tutorials in Introductory Physics
Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 24.6, Problem 1TH

Reproduced below is a side view diagram of the situation described in section II of the tutorial.

Determine an expression for the lateral magnification, m 1 = h 1 h , in terms of the object distance, x 0 , and the image distance, x i . (Hint: Draw the principal rays for the tip of the pencil and look for similar triangles. Clearly indicate the similar triangles that you use to determine your answer.)

Chapter 24.6, Problem 1TH, Reproduced below is a side view diagram of the situation described in section II of the tutorial.

Expert Solution & Answer
Check Mark
To determine

To calculate:.

The expression for the lateral magnification ml=h/h .

Answer to Problem 1TH

The expression for the lateral magnification is ml=hh=xixo.

Explanation of Solution

Given:

An object is placed before a thin lens as follows :

  Tutorials in Introductory Physics, Chapter 24.6, Problem 1TH , additional homework tip  1

Formula used :

In similar triangles ABC and DEF , corresponding sides are in equal proportions or,

AB / BC = DE / EF

AB / AC = DE /DF

Calculation:

Ray diagram showing the principal ray from the tip of pencil that is object, is given below;

  Tutorials in Introductory Physics, Chapter 24.6, Problem 1TH , additional homework tip  2

In the above diagram, two triangles given that are ΔOAC and ΔIGC .

are similar.

So that,

  IGIC=OAOC

Here,

  IG=h ….image height

  OA=h .....object height

And,

  OC=xo ......object distance

  IC=xi ......image distance

Therefore,

  hxi=hxohh=xix0

Hence, lateral magnification is given below;

  ml=hh=xixo

Conclusion:

Therefore, the lateral magnification, ml=hh=xixo .

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