Question

A camera fitted with a lens of focal length 50 mm is being used to photograph a flower that is 5 cm in diameter. The flower is placed 20 cm in front of the camera lens.
(a) At what distance from the film should the lens be adjusted to obtain a sharp image of the flower?
(b) What would be the diameter of the image of the flower on the film?
(c) What is the nature of camera lens?

Answer 1

(a)
Given:
Focal length, f = 50 mm = 5 cm
Object distance, u = $-$20 cm
Image distance, v = ?
Putting these values in lens formula, we get:

$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{v}-\frac{1}{-20}=\frac{1}{5} \\ \Rightarrow \frac{1}{v}+\frac{1}{20}=\frac{1}{5} \\ \Rightarrow \frac{1}{v}=\frac{1}{5}-\frac{1}{20} \end{gathered}$$

$$\begin{gathered} \Rightarrow \frac{1}{v}=\frac{20-5}{100} \\ \Rightarrow \frac{1}{v}=\frac{15}{100} \\ \Rightarrow v=\frac{20}{3} \\ \Rightarrow v=6.66\mathrm{cm} \end{gathered}$$

Film should be adjusted at a distance of 6.66 cm behind the lens.
(b)
Given:
Diameter of object, h = 5 cm
Diameter of image, h' = ?
Magnification, m = $\frac{h\text{'}}{h}=\frac{v}{u}$

Therefore
h' =$\frac{v}{u}xh$

h' = $\frac{6.66}{20}\mathrm{x}5=1.66\mathrm{cm}$

(c) It is a convex lens.