Question

An object 1 cm high is placed at a distance of 4 cm from a convex lens of focal length 6cm. Calculate (a) the position of the image (b) size of a image. State the characteristics of the image.

Answer 1

Height of the object (h_o) = 1 cm

Distance of the object from the lens (u) = −4 cm [∵ u is always −ive]

Focal length of the lens (f) = +6 cm [f is always +ive for a convex lens]

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

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

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

\[\Rightarrow \ \frac{1}{v} - \frac{1}{-4} = \frac{1}{6}\]

\[ \Rightarrow \ \frac{1}{v} = \frac{1}{6} - \frac{1}{4}\]

\[\Rightarrow \ \frac{1}{v} = \frac{2 - 3}{12}\]

\[ \Rightarrow \ \frac{1}{v} = -\frac{1}{12}\]

\[\Rightarrow \ v = - \ 12 \ \text{cm}\]

Thus, the image is formed at a distance of 12 cm from the lens, on the same side as the object.

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

\[\Rightarrow \ \frac{h_{i}}{1} = \frac{12}{4}\]

\[ \Rightarrow \ h_{i} = 3 \ \text{cm} \]

Thus, the height of the image is 3 cm.

The image is virtual, erect and enlarged.