Question

3
Example 7. The image of needle placed 10 cm from a
lens is formed on a wall 20 cm on the other side of the
lens. Find the focal length of the lens and size of image
formed if the size of the needle is 25 cm
Solution : Given, u=-10 cm, u = + 20 cm. f = 2,7
= ?
h = 2.5 cm​

Answer 1

Answer:

Given -

• v = 20 cm
• u = 10 cm

Now, by using lens formula -

$\\ \sf \: \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ \\ \implies \sf \: \frac{1}{f} = \frac{1}{20} + \frac{1}{10} \\ \\ \\ \implies \sf \: \frac{1}{f} = \frac{3}{20} \\ \\ \\ \implies \sf \: f = \frac{20}{3} \\ \\ \\ \implies \sf \: f = 6.67 \: cm$

Therefore, the focal length of the lens is 6.67 cm.

$\\ \sf \frac{h_1}{h_2} = \frac{v}{u} \\ \\ \\ \implies \sf \: \frac{h_2}{h_1} = \frac{20}{10} \\ \\ \\ \implies \sf \: h_2 = 2.5 \times \frac{20}{10} \\ \\ \\ \implies \sf \: h_2 = 5cm.$

Therefore, the size of the image is 5 cm.