An object is placed just at the middle point between concave mirror of radius of curvature 40 cm and a convex mirror of radius of curvature 30 cm facing each other. The mirrors are situated 50 cm apart from each other. The mirrors are situated 50 cm apart from each other. Considering the first reflection occurs in the concave mirror, determine the position and nature of the image formed by this mirror. Next find the position and nature of the image formed by the convex mirror considering the first image for concave mirror as its object.

Explanation

Focal length of the concave mirror `=(40)/(2) = 20 cm`
Focal length of the convex mirror `= (30)/(2) = 15cm`
In case of the caocave mirror, u = - 25 cm , f = - 20 cm .
`"We know", (1)/(v) + (1)/(u)= (1)/(f)`
`or, (1)/(v) + (1)/(-25) = (1)/(-20)`
`or, " " (1)/(v) = (1)/(25) - (1)/(20) = (4-5)/(100)`
`or, " " (1)/(v) = -(1)/(100)`
`or, " " v=-100 cm`
So, the image formed by the concave mirror in absence of the convex mirror would be real and intverted and situated at `Q_(1)` at a distance of 100 cm from the concave mirror. This image will act as a virtual object fot the convex mirror [Fig.1.50].

`"Here" O_(1) Q_(1) = 100cm`
Now for the presence of the convex mirror `M_(3)M_(4),`
object distance, `u_(1) = (100-50) cm = 50 cm ,`
focal lenght,` f_(1) = 15 cm`
According to the equation of mirror,
`(1)/(v_(1))+(1)/(50)=(1)/(15)`
`or, " " (1)/(v_(1))=(1)/(15)-(1)/(50)=(10-3)/(150)=(7)/(150)`
`or, " " v_(1) = (150)/(7) = 21.43 cm `
So, the final image will be formed at `Q_(2)` at a distance of 21.43 cm from the convex mirror. Positive value of `v_(1)` indicates that this image is virtual.