Question

An object 2 cm high is placed at a distance of 25 cm from the optical centre of a concave lens of focal length 15 cm. Calculate (a) the position of the image (b) the size of the image.

Answer 1

Size of the object (h_o) = 2 cm

Distance of the object from the lens (u) = −25 cm [u is always −ive]

Focal length of the lens (f) = −15 cm [f for concave lens is −ive]

Distance of the image from the lens (v) = ? [to be calculated]

Size of the image (h_i) = ? [to be calculated]

\[ \text{(a) Applying } \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]

\[ \Rightarrow \frac{1}{v} - \frac{1}{-25} = \frac{1}{-15} \]

\[ \Rightarrow \frac{1}{v} = -\frac{1}{15} - \frac{1}{25} \]

\[ \Rightarrow \frac{1}{v} = \frac{-5 - 3}{75} \]

\[ \Rightarrow \frac{1}{v} = -\frac{8}{75} \]

\[ \Rightarrow v = -\frac{75}{8} \]

\[\Rightarrow v = - \ 9.37 \ \text{cm}\]

Thus, the image is formed at a distance of 9.37 cm on the same side as the object.

\[ \text{(b) Applying } \frac{h_{i}}{h_{o}} = \frac{v}{u} \]

\[ \Rightarrow \frac{h_{i}}{2} = \frac{9.375}{25} \]

\[ \Rightarrow h_{i} = 2 \times 0.375 \]

\[ \Rightarrow h_{i} = 0.75 \ \text{cm} \]

Thus, the size of the image is 0.75 cm.