A convex mirror of focal length f forms an image1/n^th of the size of the object. The distance of the object from the mirror is

Question

A convex mirror of focal length f forms an image \(\frac{1}{n^{th}}\)of the size of the object. The distance of the object from the mirror is

A. \(\frac{n+1}{n}f\)

B. (n + 1)f

C. (n-1)f

D. \(\frac{n-1}{n}f\)

Answer 1

According to the question 

Magnification (m) =\(\frac1n\) (image is of \(\frac1{n^{th}}\) the size of object). 

Focal length = f (positive for convex mirror). 

Object distance = -u. 

Now By formula.

m = \(\frac{f}{f-u}\) 

⇒ \(\frac{1}{n} = \frac{f}{f+u}\)

⇒ f + u = nf 

⇒ u = nf – f 

⇒ u = (n-1)f. 

Therefore the object distance from the mirror is (n-1) f. Hence the option C is correct