Question

b. A convex mirror has a focal length of
18 cm. The image of an object kept
in front of the mirror is half the height
of the object. What is the distance of
the object from the mirror?​

Answer 1

Answer:

f=18 cm

m= I/O

= x/2x = 1/2

m= -v/u = 1/2

u= -2v

v= -u/2

1/f = 1/u+1/v

1/18 = 1/u - 2/u

-1/u = 1/18

u = -18

object is 18 cm in front of convex mirror

Answer 2

magnification = -v/u = 1/2 , hence u = -2v .................(1)

where u is the mirror-to-object distance and v is mirror-to-image distance.

let f be the focal length of mirror.

we have mirror formula (1/v) + (1/u) = (1/f) ...........(2)

For convex mirror f is +ve, hence using eqn.(1) and (2), (1/v) - [ 1/(2v) ] = 1/18 .....(3)

From eqn.(3), we get v = 9 cm hence u = -18 cm

hence object is at a distance 18 cm in front of mirror

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