Question

A 2.45 cm tall object is placed in 33.7 cm in front of a convex lens. The focal length

is 21.0 cm. What is the magnification of the image?

Answer 1

-1.65

Step-by-step explanation:

First of all, we find the position of the image by using the lens equation:

`(1)/(f)=(1)/(p)+(1)/(q)`

where:

f is the focal length of the lens

p is the distance of the object from the lens

q is the distance of the image from the lens

For the lens in this problem:

f = 21.0 cm (the focal length of a convex lens is positive)

p = 33.7 cm

Solving for q, we find the position of the image:

`(1)/(q)=(1)/(f)-(1)/(p)=(1)/(21.0)-(1)/(33.7)=0.0179 cm^(-1)\\q=(1)/(0.0179)=55.7 cm`

Then, the magnification of the image is given by:

`M=-(q)/(p)`

And substituting,

`M=-(55.7)/(33.7)=-1.65`

Which means that the image is inverted (negative sign) and enlarged (because M is larger than 1).