Question

A doctor examines a mole with a 15.0 cm focal length magnifying glass held 13.5 cm from the mole. Where is the image? what is its magnification? how big is the image of a 5.00 mm diameter mole?

Answer 1

1. Virtual, 135 from the lens

The distance of the image from the lens can be calculated by using the lens equation:

$\frac{1}{q}=\frac{1}{f}-\frac{1}{p}$

where

q is the distance of the image from the lens

f is the focal length

p is the distance of the mole from the lens

In this problem, we have

f = 15.0 cm is the focal length (positive for a convex lens, as the one in a magnifying glass)

p = 13.5 cm is the distance of the mole from the lens

Solving the equation for q,

$q=\frac{1}{\frac{1}{15.0 cm}-\frac{1}{13.5 cm}}=-135 cm$

The negative sign tells that the image is virtual (on the opposite side of the lens with respect to the image), and located 135 cm from the lens.

2. 10

The magnification M of the image is given by

$M=-\frac{q}{p}$

where

q = -135 cm is the distance of the image from the lens

p = 13.5 cm is the distance of the mole from the lens

Solving the equation for M, we find

$M=-\frac{-135 cm}{13.5 cm}=10$

3. 50 mm

The magnification equation can also be written as

$M=\frac{h_i}{h_o}=-\frac{q}{p}$

where

$h_i$ is the size of the image

$h_o$ is the size of the object

Since here we have

$h_o = 5.00 mm$ diameter of the real mole

M = 10

We find

$h_i = M h_o = (10)(5.00 mm)=50 mm$