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

Image distance is -52.5 cm

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

Step-by-step explanation:

u = Object distance

v = Image distance

f = Focal length = 35

m = Magnification = 2.5

`m=-(v)/(u)\\\Rightarrow 2.5=-(v)/(u)\\\Rightarrow v=-2.5 u`

Lens equation

`(1)/(f)=(1)/(u)+(1)/(v)\\\Rightarrow (1)/(35)=(1)/(u)+(1)/(-2.5u)\\\Rightarrow (1)/(35)=(3)/(5u)\\\Rightarrow u=21\ cm`

`v=-2.5* 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.