A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.
focal length of convex lens, 
= 15cm
focal length of Concave mirror, 
= 10 cm
Distance between the lens and mirror = 50cm
Distance between the object (source) and the lens = 40 cm
This implies that the point source is at focus of the mirror. Hence, two images will be formed:
One due to direct transmission of light through the lens and another due to the reflection and then transmission of the rays through the lens.
Case 1:
For the image by direct transmission
Object distance, u = -40cm
Focal length 
= 15cm
By using lens formula,
Case 2.
The rays will become parallel to the lens after refection because the object is placed at the focus of the mirror. Hence, the object distance, u= 
This implies that 
