Question

A convex mirror of focal length f produces an image of size equal to

1
/n times the size of the object.

Then the object distance is

(a) nf (b) f/
n

(c) (n + 1)f (d) (n – 1)f

Answer 1

focal length = f
magnification = 1/n

now let object was placed at a distance u = x
now we know that m = |v/u|
=> v = x/n

Applying mirror formula
1/u+1/v = 1/f
plugging the values of u,v and f
we get

-1/x + n/x = 1/f
n-1/x = 1/f
x = f(n-1)
thus the object was placed at f(n-1) distance
thus option (d) is correct

Answer 2

Answer: answer is

{n-1}f

Explanation:

Given m=1/n

Therefore m=-v/u

{Note in convex mirror v=+ve

and u=-ve}

Therefore

m = v/u

Now v/u=1/n

v=u/n

Using mirror formula

1/v + 1/u =1/f

n/u -1/u =1/f. {since u=-ve }

n-1/u=1/f

{n-1}f=u