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A convax and a concave mirror each of ra...

A convax and a concave mirror each of radius `10 cm` are placed facing eachother at `15 cm` distance. A point object is placed midway between them. Find the position of the final image if reflection takes place first at the concave mirror and then convex mirror.

Text Solution

Verified by Experts

As shown in Fig.

`P_(1)P_(2) = 15 cm`
`OP_(1) = u = - 7.5 cm`
`R = - 10cm`, for concave mirror As `(1)/(v) + (1)/(u) = (1)/(f) = (2)/(R )`
`(1)/(v) = (2)/(R ) - (1)/(u) = (2)/(-10) - (1)/(-7.5) = (-1)/(5) + (2)/(15)`
`(1)/(v) = (-1)/(15)`
`:. v = - 15 cm`, which is `P_(1)I`
Thus image `I` of object `O` is formed by concave mirror at the pole `P_(2)` of convex mirror. Hence final image is formed at the pole of convex mirror, just behind `P_(2)`.
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