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 focussed.
(a) State which type of lens is used.
(b) Calculate focal length of the lens.

Answer 1

(a) The image here can be taken on a screen. This means that the image is real. Further, we know that only convex lens forms a real image; therefore, a convex lens has been used here.

(b) Magnification (m) = 3
Object distance (u) = ?
Image distance (v) = ?
Focal length (f) = ?
Distance between image and object (v + u) = 80 cm
v = 80 $-$ u
We know that:
m = $\frac{\mathrm{v}}{\mathrm{u}}$

or 3 = $\frac{80-\mathrm{u}}{\mathrm{u}}$

or 3u = 80 $-$ u

or 4u = 80

or u = 20 cm

Thus, v = 80 $-$ u
= 80 $-$ 20 = 60 cm

Putting these values in lens formula, we get:
$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{60}-\frac{1}{-20}=\frac{1}{f} \\ \Rightarrow \frac{1+3}{60}=\frac{1}{f} \\ \Rightarrow f=\frac{60}{4}=15\mathrm{cm} \end{gathered}$$