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

Given:-

• Object height ,ho = 7cm

• Object distance ,u = -27cm

• Focal Length ,f = -18cm

To Calculate:-

• Image distance ,v
• size and nature of image .

Solution:-

By using mirror formula

→ 1/v + 1/u = 1/f

Substitute the value we get

→ 1/v + 1/(-27) = 1/(-18)

→ 1/v = 1/(-18) - 1/(-27)

→ 1/v = -1/18 + 1/27

→ 1/v = -3+2 /54

→ 1/v = -1/54

→ v = -54 cm

∴The image distance is -54cm.

Now

→ magnification ,m = hi/ho = -v/u

Substitute the value we get

→ hi/7 = - (-54)/(-27)

→ hi/7 = -54/27

→ hi = -7×2

→ hi = -14cm

∴ The height of the image is -14 cm.

The image formed is real and inverted .