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Question

As shown in the figure, an object O is at the position (10,2) with respect to the origin P. The concave mirror M1 has radius of curvature 30 cm. A plane mirror M2 is kept at a distance of 40 cm in front of the concave mirror. Consider first reflection on the concave mirror M1 and second on the plane mirror M2. Find the coordinates of the second image w.r.t the origin P.

A
(45,70)
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B
(45,70)
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C
(46,70)
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D
(46,70)
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Solution

The correct option is C (46,70)

For M1,u=10 cm,f=15 cm,h=2 cm

Using mirror formula, 1v+1u=1f
1v+110=115
1v=110115=3230
v=30 cm

and h2h1=vuh2=6 cm

The image formed by the plane mirror is 70 cm below the principal axis and 70+630=46 cm to the left of the mirror.
Therefore, coordinates of I2 w.r.t P are (-46, -70).

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