Question

how far should an object be placed from a convex lens of focal length 20cm to obtain its image at a distance of 30cm from the lens? What will be the height of the image if the object is 6cm tall?

Answer 1

from questiom we know that
f=20 , v=30, u=?
1/f= 1/v-1/u
1/20=1/30-1/u
1/20-1/30 = -1/u
3-2/60 =-1/u
1/60 =-1/u
u = -60cm

hì/hó = v/u
hi/6. = 30/-60
hi/6 = 1/-2
hi = -3cm

Answer 2

Given:

In convex lens

Focal length ,f=20 cm

Image distance,v=30 cm

Height of object,h=6 cm

To find:

Object distance from convex lens  and height of the image.

Solution:

We know that lens formula

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

Using the formula

$\frac{1}{20}=\frac{1}{30}-\frac{1}{u}$

$\frac{1}{u}=\frac{1}{30}-\frac{1}{20}$

$\frac{1}{u}=\frac{2-3}{60}$

$\frac{1}{u}=-\frac{1}{60}$

$u=-60 cm$

An object should be placed at distance 60 cm from the convex  lens.

We know that

$\frac{h'}{h}=\frac{v}{u}$

$\frac{h'}{6}=\frac{30}{-60}=-\frac{1}{2}$

$h'=6\times -\frac{1}{2}=-3 cm$

Height of image=3 cm