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Chapter 34: Q. 74 (page 993)

An object is 60cmfrom a screen. What are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object?

Short Answer

Expert verified

The radius is16cm.

Step by step solution

01

Given information

We have given,

Object distance =60cm

The lens is symmetric convergent.

Image height is twice the height of he object.

We have to find the radius of the lens.

02

Simplify

Let us consider the radius of the lens is R.

Then, using magnification we can write as the magnification for the inverted image is

m=-vu=h'h=-2v=2u=(60cm-u)u=20cm

Then, the image distance will be ,

v=60cm-20cm=40cm

The lens equation is given by,

1f=1v-1u1f=1-40cm-120cmf=403cm

The focus in term of radius of the lens is given by,

1f=(n-1)1R-1-R鈭�n=1.59鈭�340cm=(1.59-1)2RR=16cm

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