A concave mirror of focal length 10cm is placed in front of a convex mirror of focal length 20 cm. The distance between the two mirrors is 20cm. A point object is placed 5cm from the concave mirror. Discuss the formation of image.

Explanation

Let us consider the case of rays first striking the concave mirror and then the convex mirror.
Concave mirror: Here, `u=-5 cm` and `f=-10cm`
Substituting in equation
`(1)/(v) +(1)/(u) =(1)/(f)`, we get `v=10 cm`
Thus, the image is formed 10 cm behind the mirror.
This image now serves as the object for the convex mirror. However, keep ini mind that for convex mirror, all measurements will now be from the pole of this mirror. Furthermore, the sign convention for the convex mirror is shown in figure.
Convex mirror: Here, `u=-30 cm ` and `f=+20 cm`
Substituting in equation
`(1)/(v) + (1)/(u)=(1)/(f)` we get `v=12 cm`
Thus, the image if formed 12 cm behind the convex mirror. This image will now be the object for the concave mirror and the process can be repeated.
Refere to the following figure. Here, for the convex mirror:
` u=-15 cm` and `f=+20 cm`
Substituting in equation
`(1)/(v)+(1)/(u)=(1)/(f)` we get `v=+(60//7)cm`
Thus, the image is formed `(60//7)` cm behind the convex mirror
The image now serves as the object for the concave mirror.
For the concave mirror :
`u=-(20+60//7)=200//7 ` and `f=-10cm`
Substituting in the equation
`(1)/(v)+(1)/(u)=(1)/(f)`, we get `v=-200//13`
The image if formed `(200//3)` cm in front of the concave mirror.