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Question
A thin convex lens of focal length 25 cm is cut into two pieces 0.5 cm above the principal axis. The top part is placed at (0, 0) and an object placed at (– 50 cm, 0). Find the coordinates of the image.
Solution
If a symmetric lens is cut parallel to principal axis in two parts. The focal length remains the same for each part. The intensity of image formed by each part will be less compared to that of the complete lens.
If there was no cut, then the object would been at a height of 0.5 cm from the principal axis O'.
The top part is placed at (0, 0) and an object is placed at (– 50 cm, 0). There is no effect on the focal length of the lens.
u = – 50 cm, f = 25 cm, v = ?
`1/v - 1/u = 1/f`
`1/v - 1/(-50) = 1/25`
`1/v = 1/25 - 1/50`
= `(2 - 1)/50 = 1/50`
v = 50 cm
`m = (+v)/u = (+(50))/(-50)` = – 1
So the size of image is equal to that of object, m is negative so image is inverted.
So image is at (50 cm), – 1 cm) and 0.5 cm below the X – x' axis.
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