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Chapter 34: Q. 33 (page 991)

A 20-cm-tall object is 40cmin front of a converging lens that has a20cm focal length.
a Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.
bCalculate the image position and height. Compare with your ray-tracing answers in part a.

Short Answer

Expert verified

Part a

aThe image distance is s'=40cmand image height ish'=2.0cm.

Part b

bThe image distance is s'=40cmand image height is h'=2.0cm.

The both part agrees.

Step by step solution

01

Step: 1 Finding lateral magnification:  

From thin lens equation,

1s+1s鈥�=1f

The convex lens of focal lens is positive and concave lens is negative:the image virutal is negative and real image distance is positive.

The lateral magnification is

|M|=image heightobject height=h鈥�hM=鈭�s鈥�s

object height ish=2.0cm.

The lens is converging.

The distance lens object iss=40cm.

The focal length islocalid="1649230311637" f=20cm.

02

Step: 2 Finding image distance: (part a) 

The ray trace diagram is

From lens equation is

1s+1s鈥�=1f1s鈥�=1f鈭�1s1s鈥�=s鈭�fsfs鈥�=(40cm)脳(20cm)40cm鈭�20cms鈥�=40cm.

03

Step: 3 Finding image height: (part b) 

The lateral magnification lens by

M=鈭�s鈥�sM=鈭�40cm40cmM=鈭�1.|M|=h鈥�hh鈥�=h|M|h鈥�=(2.0cm)脳(1)h鈥�=2.0cm.

By comparing, the both parts are agree.

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