Question

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

Answer 1

Explanation:

Given: height of object (h)=7cm

distance of object from mirror (u)=-27cm

(minus sign as object is opposite to the direction of incident ray).

focal length (f)= -18cm

(focal length of concave mirror is negative).

Solution:

By using mirror formula:-

1/v+1/u=1/f. (here v-distance of image from mirror).

1/v = 1/f-1/u

1/v = (1/-18)-(-1/27)

1/v = -(1/18)/(1/27)

Therefore 1/v = -1/54

so, v = -54cm

Hence the mirror should be placed at 54cm in front of mirror.

Now formula for mirror magnification is:-

-V/U = M

where v- image distance

u- object distance and

m- magnification

Therefore, -(-54)/27= -2 is the magnification.

Height of image is:-

h'/h = m

h'- image height

h- object height =7cm

m- magnification = -2

h'/7 = -2

So, h' height of image is = 7 x -2

h' = -14cm

As the height is in negative this shows that the image is inverted. Also only inverted images are real therefore the image formed is real and inverted.

Thank You, I hope this will help.