# An Object of Size 7.0 Cm 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 Image. - Science

An object of size 7.0 cm 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 image.

#### Solution

Distance of the object from the mirror 'u' = −27 cm
Height of the object 'ho' = 7 cm
Focal length of the mirror 'f' = −18 cm
We have to find the distance of the image 'v' and height of the image 'hi'.
Using the mirror formula, we get

1/f=1/v+1/u

⇒ 1/-18=1/v-1/27

⇒ 1/-18=1/v-1/27

⇒ 1/27-1/18=1/v

⇒ (-1)/54=1/v

⇒ v=-54 cm

Thus, the distance of the image 'v' is 54 cm.
Now, using the magnification formula, we get

m=h_i/h_o=-v/u

h_i/i=-(-54)/(-27)=-2/1

h_i=-14 cm

Therefore, the height of the image 'hi' is 14 cm.
Again, using the magnification formula, we get

m=-v/u=-((-54))/((-27))

m=-2

Thus, the image is real, inverted and large in size.

Concept: Concave Mirror
Is there an error in this question or solution?

#### APPEARS IN

Lakhmir Singh Class 10 Physics (Science)
Chapter 4 Reflection of Light
Q 17 | Page 198