Question

Magnification produced by a convex mirror is 1/n . If the focal length is 'f' , find the object distance, image distance in terms of curvature 'r'.

Answer 1

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Given,

Magnification, m = 1/n

Focal length = f

Object distance, u =?

Image distance, v =?

Curvature = r

So, f = r/2........ (1)

Now,

Since, m = 1/n

=> - v/u = 1/n

=> u = - vn......... (2)

Now, 1/v + 1/u = 1/f [Using Mirror formula]

=> 1/v - 1/vn = 1/f [From (2)]

=> n - 1/vn = 1/f

=> f = vn/n - 1

=> r/2 = vn/n - 1 [From (1)]

=> r (n - 1) = 2vn

=> v = r (n - 1)/2n units

So, u = - vn = - r(n - 1)/2n ×n

= - r/2 ( 1 - n) units

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$\huge \bold{Answer :}$
- r/2 (1 - n) units.

Answer 2

Given, magnification, m = 1/n

Focal length = f

Object distance, u

Image distance, v

Curvature = R

So, f = R/2........ (1)

m = 1/n

=> - v/u = 1/n

=> u = - vn......... (2)

Now, 1/v + 1/u = 1/f [Using Mirror formula]

=> 1/v - 1/vn = 1/f [From (2)]

=> n - 1/vn = 1/f

=> f = vn/n - 1

=> R/2 = vn/n - 1 [From (1)]

=> R (n - 1) = 2vn

=> v = R (n - 1)/2n units

So, u = - vn = - R(n - 1)/2n ×n

= - R/2 ( 1 - n) units

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