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Question
Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.
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Solution
We know for a concave mirror, f < 0 [negative] and u < 0 [negative]
2f < u < f
∴ `1/(2"f") > 1/"u" > 1/"f"`
or `(-1)/(2"f") < (-1)/"u" < (-1)/"f"`
or `1/"f" - 1/(2"f") < 1/"f" - 1/"u" < 1/"f" - 1/"f"`
or `1/(2"f") < 1/"v" < 0 ...[∵ 1/"f" - 1/"u" = 1/"v"]`
This implies that v < 0 forms an image on the left.
Also, 2f > v .....[∵ 2f and v are negative]
|2f| < |v|
So, the real image is formed beyond 2f.
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