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A convex lens forms a real and inverted image of a needle at a distance of $50 cm$ from it. Where is the needle placed in front of a convex lens, if the image is equal to the size of the object. Find the power of the lens.

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2 D

1 D

4 D

0.5 D

answer is C.

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Detailed Solution

A convex lens forms a real and inverted image of a needle at a distance of

50 cm

from it, so that the size of the image is equal to the size of the object. The power of the lens is

4 D .

Given that,
Image distance

(v) = 50 cm

Magnification

(m) = - 1

So, we will apply the formula

m = \frac{v}{u}

From here we will determine the “

u

”

u = \frac{50}{- 1}

\Rightarrow u = - 50 cm

So, the needle is placed

50 cm

in front of the lens.
Now, to find the power first we will find the value of

“ f ”

.
So, we will apply the lens formula:

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

Where,

v = 50 cm

u = - 50 cm

\Rightarrow \frac{1}{f} = \frac{1}{50} - \frac{1}{- 50}

\Rightarrow f = 0.25 m

Now, to find the power of the lens we will apply the power formula.

P = \frac{1}{f}

\Rightarrow P = \frac{1}{0.25}

\Rightarrow P = 4 D

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