Question

radius of concave mirror is 40 CM and the size of the image is twice as that of object then object distance is?

Answer 1

we have

R = 40cm

then,

f = R/2 = 40/2 = 20 cm,

now, as the mirror is concave in nature, the focal length will be

f = -20 cm

let size of object be x, then size of image is 2x

h2/h1= -v/u

2x/x =-v/u

so, we have

u = -v/2

also, we know that for a curved mirror

1/f = 1/v + 1/u

1/f = 1/v + 1/(-v/2)

1/-20 = 1/v - 2/v

or

-1/20 = -1/v

thus, image distance will be

v = 20 cm

Answer 2

R=-40cm
then f=C/2
f=-20cm
ho=?
hi=2ho
v=?
u=?
m= -v/u or hi/ho
therefore -v/u=hi/ho
-v/u=2ho/ho
-v=2u
v= -2u
by using mirror formula i.e.
1/f = 1/v + 1/u
-1/20 = -1/2u + 1/u
-1/20 = -1+2/u
-1/20 = 1/u
u= -20cm