Question

A concave mirror of focal length 15 cm forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be
(a) 22.5 cm(b) 7.5 cm(c) 30 cm(d) 45 cm

Answer 1

answer : option (b) 7.5cm

explanation : focal length of concave mirror, f = -15cm

a/c to question, linear dimension of image is two times of object. and also image is virtual
e.g., if size of object is h
then, size of image is 2h

so, magnification, m = linear dimension of image/linear dimension of object [ don't confuse , " linear dimension " is nothing just size of image/object ]

so, m = 2h/h = 2 = -v/u [ formula , m = -v/u ]

so, v = -2u

now, 1/v + 1/u = 1/f

or, 1/-2u + 1/u = 1/-15

or, 1/2u = 1/-15

u = -15/2 = -7.5cm

hence, object distance is 7.5cm