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Question

A professor reads a greeting card received on his 50th birthday with +2.5 D glass keeping the card 25 cm away. Ten years later, when he reads his farewell letter with the same glasses, he has to keep the letter 50 cm away. The power of lens the professor should use now is

A
3 D
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B
4 D
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C
4.5 D
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D
6 D
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Solution

The correct option is C 4.5 D
The professor reads the card at a distance 25 cm using a glass of +2.5 D.

Since power of a lens is reciprocal of its focal length, we can write that
f=12.5=40 cm

After ten years, when he reads farewell letter, he keeps the letter at a distance 50 cm.
u=50 cm

Now using lens formula,

1v1u=1f

1v=1u+1f

Substituting the given data we get,

1v=150+140

v=200 cm

To read the farewell letter at a distance of 25 cm [near point]

u=25 cm

Again using lens formula,

1v1u=1f

1f=12001251f=9200

f=29 m

Thus, required power of lens =1f=92=4.5 D.

Hence, option (c) is the correct answer.

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