Question

A convex mirror of focal length $f$ produces an image $({\dfrac{1}{n}})^{th}$of the size of the object. Then the distance of the object from the mirror is:-
$(a) \: nf$
$(b) \: (n + 1)f$
$(c) \: (n - 1)f$
$(d) (\dfrac{n}{n + 1} )f$

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Answer 1

Answer:-

(c). (n - 1)f

Explanation:-

Given that:-

→Focal length of the mirror = f

→Size of the image with respect to size

of the object = (1/n) th

Now, we know the mirror formula:-

=> m = f/f-u

Where:-

• m is magnification of the image

• f is focal length of the mirror

• u is the distance of the object from the

mirror.

As per Sign Convention of convex mirror :-

• u will be -ve.

• f will be +ve.

Now, let's find the answer by using the above formula.

=> 1/n = f/ [f-(-u]

=> 1/n = f/f+u

=> nf = f + u

=> u = nf - f

=> u = (n - 1)f

Thus, distance of the object from the mirror is (n - 1)f. [option. c]