Question

A convex lens of focal length 35 cm produces a magnified image 2.5 times the size of the object. What is the object distance if the image (formed) is real?

Answer 1

Answer:

Image distance is -52.5 cm

Image is virtual and forms on the same side of the lens and upright image is formed.

Explanation:

u = Object distance

v = Image distance

f = Focal length = 35

m = Magnification = 2.5

$m=-\frac{v}{u}\\\Rightarrow 2.5=-\frac{v}{u}\\\Rightarrow v=-2.5 u$

Lens equation

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{35}=\frac{1}{u}+\frac{1}{-2.5u}\\\Rightarrow \frac{1}{35}=\frac{3}{5u}\\\Rightarrow u=21\ cm$

$v=-2.5\times 21=-52.5\ cm$

Image distance is -52.5 cm

Image is virtual and forms on the same side of the lens and upright image is formed.