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Question 2
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.


Solution

Image distance, v = 50 cm
We know that, m = - vu
m = 1
1 = - 50u
Thus, u = - 50 cm
Object distance, u = - 50 cm
focal length = f
According to the lens formula,
u = - 50 cm
v = + 50 cm
f = ?
1f = 1v1u
1f = 150 + 150
f = + 25 cm = 0.25 m
Power of lens (P) = 1f = 10.25 = + 4D.

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