# 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

2015-02-15T14:49:07+05:30

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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

thank u so much for your answer , it really helped me a lot
2015-02-15T16:12:10+05:30
The image can be virtual or real so accordingly 2 case will arise.
using mirror formula we find that the focal length is 15 cm & the mirror is concave