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Q

A convex lens of focal length $20\:cm$ produces images of the same magnification $2$ when an object is kept at two distances $x_{1}\:\:and\:\:x_{2}(x_{1}>x_{2})$ from the lens . The ratio of $x_{1}\:\:and\:\:x_{2}$ is :

• Option 1)

$2:1$

• Option 2)

$3:1$

• Option 3)

$5:3$

• Option 4)

$4:3$

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By using lens formula

$\frac{1}{2X_1}-\frac{1}{-X_1}=\frac{1}{20}$

$\Rightarrow X_1=30$

$\\\frac{1}{-2X_{2}}-\frac{1}{-X_{2}}=\frac{1}{20}\\\\\\\:\Rightarrow X_{2}=10$

$\Rightarrow X_{1}:X_{2}=30:10=3:1$

Option 1)

$2:1$

Option 2)

$3:1$

Option 3)

$5:3$

Option 4)

$4:3$

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