Question

An object of size 7cm is placed at 27 cm in front of a concave mirror of focal length 18 cm . At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and nature of the image.

Answer 1

We know that, for a concave mirror the focal length will be negative.
Therefore, given: u = -27cm     f = -18cm    h(object size) = 7cm


( Note that the distance at which you will obtain sharp image will be your "v" i.e.  the object distance for that  image formation which is required in the question)

hence,
1/v + 1/u = 1/f                                       (mirror formula)
1/v + (1/(-27)) = 1/(-18)
1/v  =   1/27 + 1/-18                              ( LCM of 18 and 27 is 54)
1/v  =  1/(-54)
v     =  -54cm
image distance = -54cm
hence, image is formed on the same side.

now we know,
h'/h = -v/u                                             (h' denotes object height)
h'/7 = -(-54)/-(27)
h'    =  7 * (-2)
h'    =  -14cm

hence, image is inverted (since h' is negative) and it is on the same side of that of the object (since v is negative).

HOPE IT HELPS .

Answer 2

HERE IS YOU ANSWER

SO ACCORDING TO THE QUESTION

U = -27

F = -18

H = 7

SO WE HAVE TO FIND V

BY FORMULA

1/V + 1/U = 1/F

1/V = -1/54

V = -54

SO NEXT WE HAVE TO DO

H1/H=-V/U

H1/7=54/-27

H1 = -14 CM