A convex mirror of focal length f forms an image \(\frac{1}{n^{th}}\)o

1.	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 isA. \(\frac{n+1}{n}f\)B. (n + 1)fC. (n-1)fD. \(\frac{n-1}{n}f\)
Answer» 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

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 isA. \(\frac{n+1}{n}f\)B. (n + 1)fC. (n-1)fD. \(\frac{n-1}{n}f\)

Answer»

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