A real image obtained by a concave mirror is 4 times bigger than the object. If the object is displaced by 3 cm away from the mirror, the image size becomes 3 times the object size. Find the focal length of the mirror.

Explanation

`rArr` Here, magnification of image m = - 4
New magnification of image m = -3
Focal lenght f = ?
Focal lenght f= ?
AS per Gauss formula
`1/f = 1/v + 1/u`
`therefore u/f = (1)/(-m) + 1`
`therefore u/f = 1 (1)/(m) " " (therefore m = -4)`
`therefore u/f = 1 - (1)/(-4)`
`therefore u/f = 1 + (1)/(4)`
`therefore u/f = 5/4`..........(1)
`rArr` When object is placed 3 cm away from mirror,
`therefore (u+3)/(f) = 1 + (1)/(3)`
`therefore (u+3)/(f) = (4)/(3)`
`therefore u/f + 3/f = 4/3`
`therefore 5/4 + 3/f = 4/3` [ From (1)]
`therefore 3/f = 4/3 - 5/4`
`therefore 3/f = (16-15)/(12)`
`therefore 3/f = 1/12 therefore f = 36 cm = 360 cm `