Question

An object of length 4 cm is placed in front of a concave mirror at distance 30 cm. The focal length of mirror is 15 cm.

1. Where will the image form?
2. What will be the length of image?

Answer 1

O = 4 cm

u = -30 cm

f = -15 cm

From mirror formula , 

`1/"f" = 1/"v" + 1/"u"`

∴ `1/"v" = 1/"f" - 1/"u"`

∴ `1/"v" = 1/(-15) - 1/(-30) = 1/30 - 1/15`

∴ `1/"v" = (-1)/30`

∴ v = -30 cm

Hence , the image is formed at a distance of 30 cm in front of the mirror .

m = `-"v"/"u" = "I"/"O"`

∴ I = `"-OV"/"u" = (-4 xx -30)/(-30) = -4`cm

Negative sign indicates inverted image.

So, I = 4 cm

Hence , the length of the image is 4 cm.