A concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is 6cm, find the shift of screen.

Explanation

In first case, `1/x + 1/(3x) = 1/f` , where x = object distance and 3x = image distance.
In second case, `1/(x+5) + 1/(2(x+5)) = 1/f`
As the magnification decreases, shift of object must be away from mirror and hence the object distance now equals to x+5
solving the two equations we get
f= 30cm
Shift the screen = 2[x+5] - 3x= -30cm.