Question

Question 10
An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.

Answer 1

Object distance, u = - 25 cm
focal length, f = 10 cm
height of the object, $h_0$ = 5 cm
Substituting in the lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$
$\frac{1}{v}=\frac{1}{10}-\frac{1}{25}$
$\frac{1}{v}=\frac{3}{50}$
$v=\frac{50}{3}cm$ = 16.7 cm
The image is real and inverted at a distance of 16.7 cm from the lens on the opposite side.
Magnification, $m=\frac{h_i}{h_0}=\frac{v}{u}$
$\frac{h_i}{5}=\frac{16.7}{-25}$
$h_i=\frac{16.7}{-25}\times 5$= -3.34 cm
The image is formed at a distance 16.7 cm from the lens on the other side of the lens. The image is inverted and diminished.