Question

a convex mirror has a focal length of 20cm find the position of object for which image will be half of the size of the object

Answer 1

Given f=20cm  

m=1/2  

but,m=-v/u  

1/2=-v/u  

v=-u/2  

1/v=-2/u  

We know 1/f=1/u+1/v  

=1/20=1/u-2/u  

=-1/u=1/20  

=u=-20  

The answer is 20 cm behind the lens.

Hope it helps

Answer 2

Answer:

1. Focal length = 20
2. Object distance =?
3. Image distance = ?

4. Magnification = 1/2

Explanation:

using the mirror formula m = - v/ u

we have ,

m = 1/2

1/2 = -v/u

cross change

1/v = -2/u

v = -2/u • • • • •(1)

we know that : 1/f = 1/v + 1/u

f= 20

v = -2/u

1/20 = 1/u + ( -2/u )

1 /20 = -1/u

u= 20