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Chapter 35: Q. 32 (page 1018)

A 15cm-focal-length converging lens is 20cmto the right of a 7.0cm-focal-length converging lens. A 1.0cm-tall object is distance L to the left of the first lens.

a. For what value of L is the final image of this two-lens system halfway between the two lenses?

b. What are the height and orientation of the final image?

Short Answer

Expert verified

a. Value of L is L=14cm.

b. The height and orientation of the final image is M=-1.7cm.

Step by step solution

01

Part (a) Step 1: Given Information.

We need to find out the object is distance L of the first lens.

02

Part (a) Step 2: Calculation.

Since:

f1=7cmf2=15cm

Here, f1and f2is the focal length of first and second lens respectively.

Firstly, Let us find the initial position of the object for the second lens:

role="math" localid="1650112585802" 1S1+1S2'=1f21S21=1f2-1S21S2'=115-1-101S2'=16S2'=6cm鈫�realimage

Here, S2and f2is distance of the object from the lens and the focal length of the second lens respectively.

03

Part (b) Step 1: Given Information.

We need to find the height and orientation of the final image.

04

Part (b) Step 2: Calculation.

Let us find Magnification:

M=M1M2M=-S1'S1-S1'S2M=S1'S2'S1S2M=(14)(-10)(14)(6)M=1.7cm

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