Question

the focal length of a convex lens is 30 cm and the size of the image is half of the object . the object distance is ?
a- 60 cm b- 90 cm
c- 30 cm d- 40 cm
and why?
please help me fast!

Answer 1

magnification(m)=V/U
Where V is image distance and
U is object distance

You have m=1/2
So, V/U=1/2
or, U=2V

Also,\[\frac{1}{f}=\frac{1}{U}+\frac{1}{V}\]where, f is focal length

So, you now have,\[\frac{1}{30}=\frac{1}{2V}+\frac{1}{V}\]Solve for V...
That is your answer!