Two concave mirrors each of radius of curvature 40cm are placed such that their principla axes are parallel to each other and at a distance of 1cm to each other. Both the mirrors are at a distance of 100cm to each other. Consider first reflection at `M_(1)` and then at `M_(2)` , find the coordinates of the image thus formed. Take location of object as the origin

Answer

12 cm , -0.6 cm

Explanation

f= -20 cm ,`(1)/(v) + (1)/((-60)) = (1)/((20))`
`(1)/(v) = (1)/(60) - (1)/(20) = (-40)/(60 xx 20) implies v = -30`
`m= -(v)/(u) = ((-30 xx -1))/((-60)) = (-1)/(2)`
So image coordinates are (-30 , 3/2)
At `m_(2)`:
`(1)/(v) + (1)/((70)) = (1)/(-20) implies (1)/(v) = (1)/(70) - (1)/(20) = (-50)/(70 xx 20)`
`v = (-140)/(5)` = -28 cm
So magnification = `(-v)/(u) = ((-28)(-1))/((-70)) = -(2)/(5)`
Object length = `(3)/(2)` cm
image length = `((3)/(2))((2)/(5))= (3)/(5)cm`
below axis of `M_(2) : y = (-(3)/(5))`
x coordinate = `(40-28) = 12`
so coordinates = `(12, -(3)/(5))`