To find the co-ordinates of image of point object P formed after two successive reflection at concave mirror and then at convex.
Consider concave mirror (M1) from figure,
Object distance, u1=−20cm
Focal length of the mirror, f1=−15cm
Applying mirror formula,
Magnification, m1=−v1u1=−(−60)(−20)=−3 (image is inverted)
The height at which the image point will be m1×AP=3×2=6mm
The image formed by concave mirror acts as object for convex mirror.
Now, at convex mirror (M2) from figure
Object distance, u2=+10cm
Focal length of the mirror, f2=20cm
Applying mirror formula, we get
Hence the final position of image after two successive reflection at concave mirror and then at convex 20 cm in front of convex mirror, M2
So the image of the point will be formed above, m2×C′P′=2×8=16mm
So the required coordinates of the image is, P(30,−14)