In the displacement method, a convex lens is placed in between an obect and a screen. If the magnification in the two positions are `m_(1) and m_(2)` and the displacement of the lens between two positions is x, then the focal length of the lens is:

Options

A. `(x)/(m_(1)+m_(2))`
B. `(x)/(m_(1)-m_(2))`
C. `(x)/((m_(1)+m_(2))^(2)`
D. `(x)/((m_(1)-m_(2))^(2)`

Answer

B

Explanation

(b) `m_(1) = (v)/(u) m_(2) = (u)/(v)`
`(1)/(f) = (u-v)/(uv)`
`(1)/(f)=((u-v)(v+u))/(uv(v+u))`
`f = (uv(v+u))/(u^(2)-v^(2))`
`therefore " " f=(v+u)/(u^(2)/(uv)-(v^(2))/(uv))=(u+v)/((u)/(v)-(v)/(u))`
`therefore " " f = (x)/(m_(2) - m_(1))`.