Question

The focal length of a convex lens is 25 cm. At what distance
from the optical centre of the lens an object be placed to
obtain a virtual image of twice the size
​

Answer 1

Answer:

$\large\tt\color{pink}\underline{\underline{Question:}}$

$\textsf{The focal length of a convex lens is 25 cm.}$

$\textsf{At what distance from the optical center of}$

$\textsf{of the lens an object be placed to obtain}$

$\textsf{a virtual image of twice the size}$

$\large\tt\color{blue}\underline{\underline{Given:}}$

$\textsf{Length of a convex lens = 25 cm}$

$\textsf{Size placed obtain a virtual image is twice}$

$\large\tt\color{green}\underline{\underline{To\:find:}}$

$\textsf{Distance from the optical center of the lens}$

$\large\tt\color{cyan}\underline{\underline{We\:know:}}$

$\bold{Magnification=\frac{Height of the image}{Height of the object}}=2$

$\textsf{Let Magnification be m}$

$\textsf{Let height of the image be y}$

$\textsf{Let height of the object be x}$

$\large\tt\color{red}\underline{\underline{Solution:}}$

$\bold{m=\frac{y}{x}=2}$

$\Rightarrow\bold{\frac{y}{x}=2}$

$\textsf{Multiply x into 2}$

$\Rightarrow\bold{y=2x}$

$\textsf{Use the lens}$

$\textsf{Let the length of convex lens be f}$

$\Rightarrow\bold{f=\frac{1}{y}-\frac{1}{x}}$

$\Rightarrow\bold{\frac{1}{25}=\frac{1}{2x}-\frac{1}{x}}$

$\Rightarrow\bold{\frac{1}{25}=\frac{1-2}{2x}}$

$\Rightarrow\bold{\frac{1}{25}=\frac{-1}{2x}}$

$\Rightarrow\bold{x=\frac{-1}{2}÷\frac{1}{25}}$

$\Rightarrow\bold{x=\frac{-1}{2}×\frac{25}{1}}$

$\Rightarrow\bold{x=-12.5cm}$

So , the negative sign shows that the image is of the lens ....

HOPE IT HELPS YOU