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 A thin convex lens of focal length ‘f’ is put on a plane mirror as shown in the figure. When an object is kept at a distance ‘a’ from the lens - mirror combination, its
image is formed at a distance  \frac{a}{3}  in front of the combination. The value of ‘a’ is :

 

  • Option 1)

    f

  • Option 2)

    2f

  • Option 3)

    3f

  • Option 4)

    \frac{3}{2}f

 

Answers (1)

best_answer

As we learnt in

Thin lens formula -

\frac{1}{v}-\frac{1}{u}= \frac{1}{f}

 

- wherein

u \, and \, v are object and image distance from lens.

 

 When object is kept at distance a from thin convex lens.

By lens formula

\frac{1}{v}=\frac{1}{f}-\frac{1}{a}                                    (i)

Mirror forms image at equal distance from mirror

From lens formula

\frac{3}{a}-\frac{1}{v}=\frac{1}{f}

\frac{3}{a}-\frac{1}{f}+\frac{1}{a}=\frac{1}{f}

After solve we get 

a = 2f  

Correct option is 2.

 

 


Option 1)

f

This is an incorrect option.

Option 2)

2f

This is the correct option.

Option 3)

3f

This is an incorrect option.

Option 4)

\frac{3}{2}f

This is an incorrect option.

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