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Question

Find the co-ordinates of image of point object P formed after two successive reflection at concave mirror and then at convex.
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Solution

To find the co-ordinates of image of point object P formed after two successive reflection at concave mirror and then at convex.
Solution:
Consider concave mirror (M1) from figure,
Object distance, u1=20cm
Focal length of the mirror, f1=15cm
Applying mirror formula,
1f1=1v1+1u11v1=1f11u11v1=1151201v1=4+360v1=60cm
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
1f2=1v2+1u21v2=1f21u21v2=1201101v2=1220v2=20cm
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
Magnification m2=v2u2=(20)10=+2
So the image of the point will be formed above, m2×CP=2×8=16mm
So the required coordinates of the image is, P(30,14)

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