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Chapter 34: Q. 69 (page 993)

A lightbulb is 3.0 m from a wall. What are the focal length and the position (measured from the bulb) of a lens that will form an image on the wall that is twice the size of the lightbulb?

Short Answer

Expert verified

The focal length is 67 cm and the position of the lens is 100 cm from the lightbulb.

Step by step solution

01

Step 1. Given information is :Distance between light bulb and the wall = 3.0 mImage of the light bulb is twice it's size h' = 2h

We need to find out the focal length and the position of the lens.

02

Step 2. Applying the concept of magnification

M=h'hh'=2hM=2hh=2

Magnification in terms of image and object distance can be represented as :

M=-s'sWeknowthat,s+s'=300cms'=300cm-sM=-300cm-ss-2=-300cm-ss2s=300cm-s3s=300cms=100cmTherefore,s'=300-s=300cm-100cm=200cm

Now, Using thin lens formula,

1s+1s'=1f1f=s'+sss'f=ss's'+sf=(100cm)(200cm)200cm+100cmf=2000cm300cm=67cm

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