A convex lens of focal length f is placed somewhere in between an object and a screen. The distance between the object and the screen is x. If the numerical value of the magnification produced by the lens is m, then the focal length of the lens is

Question

A convex lens of focal length f is placed somewhere in between an object and a screen. The distance between the object and the screen is x. If the numerical value of the magnification produced by the lens is m, then the focal length of the lens is (A) (m x/(m+1)2) (B) (m x/(m-1)2) (C) ((m+1)2/m) x (D) ((m-1)2/m) x

Tardigrade Admin · Accepted Answer

(v/-u)=-m and v+u=x ⇒ u=(x/1+m) (1/f)=(1/v)-(1/u) ⇒ f=(m x/(m+1)2)

Q. A convex lens of focal length $f$ is placed somewhere in between an object and a screen. The distance between the object and the screen is $x$ . If the numerical value of the magnification produced by the lens is $m$ , then the focal length of the lens is

$\frac{m x}{( m + 1 ) ^{2}}$

$\frac{m x}{( m - 1 ) ^{2}}$

$\frac{( m + 1 ) ^{2}}{m} x$

$\frac{( m - 1 ) ^{2}}{m} x$

$\frac{v}{- u} = - m$ and $v + u = x$
$\Rightarrow u = \frac{x}{1 + m}$
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\Rightarrow f = \frac{m x}{( m + 1 ) ^{2}}$

Q. A convex lens of focal length f is placed somewhere in between an object and a screen. The distance between the object and the screen is x. If the numerical value of the magnification produced by the lens is m, then the focal length of the lens is

(m+1)2mx​

(m−1)2mx​

m(m+1)2​x

m(m−1)2​x