A plane mirror is placed 22.5 cm in front of a concave mirror of focal length 10 cm. Find where an object can be placed between the two mirrors, so that the first image in both the mirrors by concave mirror.Also find out magnification of the image produced by concave mirror

Explanation

Let the object is placed at a distance from the concave mirror = x
distance fo the object from the plane mirror `= (22.5 - x)`
So plane mirror will from equal and erect image of object at a distance `(22.5 -x)` behind the mirror
Since the image formad by concave mirror coincides with the image formed by plane mirror hence for concave mirror
` v=- [22.5 + (22.5 -x)] =- (45 - x)`
and `u=-x`
`:. , (1)/( -(45 -x)) + (1)/( -x) = (1)/(-10)`
or `(45)/((45 x- x^(2)) = (1)/(10)`