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In a concave mirrorr experiment, an obje...

In a concave mirrorr experiment, an object is placed at a distance `x_(1)` from the focus and the image is formed at a distance `x_(2)` from the focus. The focus length of the mirrorr would be

A

`x_(1)x_(2)`

B

`sqrt(x_(1)x_(2))`

C

`((x_(1)+x_(2)))/(2)`

D

`sqrt((x_(1))/(x_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
For concave mirror , `(1)/(v) + (1)/() = (1)/(f) rArr = f = (vu)/(v + u)`
Given, `u = (f + x_(1)) + v = (f + x_(2))`
`therefore " " f=(vu)/(v+u)=((f+x_(1))(f+x_(2)))/((f+x_(1))(f+x_(2)))`
`rArr " " f=(t^(2)+fx_(2)+fx_(1)+x_(1)x_(2))/(2f+x_(1)+x_(2))`
`rArrr " " 2I^(2)+fx_(1)+fx_(2)=f^(2)+fx_(2)+fx_(1)+x_(1)x_(2)`
`f^(2) = x_(1)x_(2)rArrf=sqrt(x_(1)x_(2))`
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