Question

An image formed on a screen is three times the size of the object. The object and screen are 80 cm apart when the image is sharply focused.

(a) State which type of lens is used.

(b) Calculate the focal length of the lens.

Answer 1

(a)

The image is sharply focused on the screen so the lens used is a convex lens.

(b)

Step 1, Given data

The distance between object and screen = u+v = 80 cm

And, magnification, m =3

Step 2, Finding the focal length

We know,

Magnification is given as

m = $\frac{v}{u}=3$

Or,

$v=3u$

Now we can write

u + v = 80

Or, u + 3u = 80

Or, 4u = 80

Or, u = 20 cm

Then, v = 60 cm

Using sign convention, u = -20 cm and v = 60 cm

Now, using lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Putting all the values

$\frac{1}{f}=\frac{1}{60}-\frac{1}{-20}=\frac{1}{15}orf=15cm$

Hence the focal length of the lens is 15 cm