Question

The focal length of a concave mirror is 10 cm.find position of the object in front of the mirror so that the image is 1/5 th times the size of the object

Answer 1

Answer is 40cm as using mirror formula

Answer 2

The asked question points to a real image of magnification (m)=2,Taking the normal sign convention of direction of incident light to be positive, here both u&v are negative with focal length is also negative. m=2=>(-v)/(-u)=2=> u=v/2 so from the mirror formulae 1/v+1/u=1/f,where f=(-)10cm =>1/u+1/v=2/v+1/v=1/((-10)=>3/v=(-1/10)=>v=-10/3 or 3.33cm.So the screen is to be placed at 3.33 cm from mirror, where as object is to be placed at 1.665 cm from the mirror on optical axis.