Question

how far should an object be form concave of focal length 20cm to form a real image 1/5th its size?​

Answer 1

hey there.,

f=-20

h'/h=-1/5=-v/u

u=5v

1/f=1/v+1/u

1/-20=1/v+1/5v

1/20=6/5v

5v=-120

v=-24

u=5v

-120cm

hope it helps.........................................

Answer 2

Given--

Focal length of concave mirror,f = – 20cm ( – ive for concave mirror)

Size of image ,I = 1/5 of size of object = 1/5 * O,

where,I = size of image

O = size of object

object distance, u = ?

image distance = v

Solution ---

Magnification,m is given as,

m = I/O = – v/u ( ratio of size of image to size of object which is equal to ratio of image distance to object distance)

1/5 = – v/u

or, v = – u/5

now applying the mirror formula,

1/f = 1/u + 1/v

– 1/20 = 1/u – 5/u

1/20 = 1/u + 5/u as image is real so v will be negative so on putting its value it becomes positive

or, u= – 120cm

i can show you how to do it