Verified Solution Science Light – Reflection and Refraction NCERT Class 10th · Ch 9

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? Also, find the power of the lens.

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Answer

A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. The image is equal in size to the object, which means the object is placed at a distance of 2F from the lens. So, the object is also placed 50 cm in front of the lens.

Using the lens formula:
1/f = 1/v - 1/u

Here,
v = +50 cm (real image, so positive)
u = -50 cm (object is in front of the lens, so negative)

So  1/f = 1/50 - (-1/50)
=>  1/f = 1/50 + 1/50 = 2/50 = 1/25

So, the focal length f = 25 cm

Now,
Power of the lens (P) = 100 / focal length (in cm)
P = 100 / 25 = 4 dioptres

Hence:
The needle is placed 50 cm in front of the lens.
The power of the lens is +4 dioptres.

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