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

 

Answers (1)

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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