#
Real image 1/5th size of object is formed at a distance of 18 cm from the mirror. what is the nature of mirror ? calculate its focal length .

2
by pankhudi

Log in to add a comment

by pankhudi

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

M = +1/5 or -1/5 and v = +18 cm or -18 cm

So there are 4 possibilities. But v positive means behind convex mirror and hence, the image has to be erect. Hence m is positive only. There are 3 cases only.

It is a mirror: m = -v/u 1/f = 1/v + 1/u

case 1)

m = +1/5 = -v/u let v = +18 cm

u = - 5 v = -90 cm

1/f = 1/18 - 1/90 = 4/90 => f = +22.5 cm Convex Mirror.

case ii)

m = +1/5 = -v/u let v = -18 cm

u = +90 cm not possible. as u is always negative.

case iii)

m = -1/5 = -v/u let v = +18 cm

u = +90 cm not possible

case iv)

m = -1/5 = -v/u u = 5 v

v = -18 cm

1/f = -1/18 - 1/90 = -6/90

f = -15 cm concave mirror

So there are 4 possibilities. But v positive means behind convex mirror and hence, the image has to be erect. Hence m is positive only. There are 3 cases only.

It is a mirror: m = -v/u 1/f = 1/v + 1/u

case 1)

m = +1/5 = -v/u let v = +18 cm

u = - 5 v = -90 cm

1/f = 1/18 - 1/90 = 4/90 => f = +22.5 cm Convex Mirror.

case ii)

m = +1/5 = -v/u let v = -18 cm

u = +90 cm not possible. as u is always negative.

case iii)

m = -1/5 = -v/u let v = +18 cm

u = +90 cm not possible

case iv)

m = -1/5 = -v/u u = 5 v

v = -18 cm

1/f = -1/18 - 1/90 = -6/90

f = -15 cm concave mirror

using mirror formula we find that the focal length is 15 cm & the mirror is concave