Question

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 the convex lens, if the image is equal to the size of the object​

Answer 1

Answer:

Object distance, u= – 50 cm

Image distance, v= 50 cm

Focal length = f

According to the lens formula,

u = -50 cm v = + 50 cm. f =? 1/f = 1/v €“ 1/u 1/f = 1/50 + 1/50 f = + 25 cm. = 0.25 m Power of lens (P) = 1/f = 1/ 0.25 = + 4D.

Answer 2

Given:

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A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it.

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To find:

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Place where the needle placed in front of the convex lens, if the image is equal to the size of the object.

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Solution:

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Here in the question it is given that the size of the image is equal to the size of the object. So, magnification of the image will be 1.

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m = – 1

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v = 50 cm

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We need to calculate u and f.

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Here m means magnification, v means distance of the image from lens.

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u means distance of the object from the lens and f means focal length of the lens.

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Magnification is negative for real image and v is positive because it is real image.

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We know that,

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Magnification = Distance of the image/Distance of the object.

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$:\displaystyle\implies \displaystyle \: m = \frac{v}{u}$

$:\displaystyle\implies \displaystyle \: - 1 = \frac{50 \: cm}{u}$

u = – 50 cm.

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Hence, distance of the object from lens is 50 cm.

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Now, by applying lens formula we will find focal length of the lens.

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1/f = 1/v – 1/u

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$:\displaystyle\implies$ 1/f = 1/50 – 1/–50

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= 1/50 + 1/50 = 2/50 = 1/25

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1/f = 1/25

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$:\displaystyle\implies$ f = 25 cm.