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  • 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.

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 \left ( 0,0 \right ) and an object placed at \left ( -50\; cm,0 \right ). Find the coordinates of the image.

 

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The focal length will remain the same for each of the parts in case an asymmetric lens is cut in two parts parallel to the principle axis. In such a case the intensity of image that has been formed by every part will be lower in comparison to that of the complete lens.

If there was no cut, then the object would have been at the height of 0.5 cm from the principal axis OO'

The top part is placed at \left ( 0,0 \right ) and an object placed at \left ( -50\; cm,0 \right ). There is no effect on the focal length of the lens.

Applying lens formula,

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

\frac{1}{v}=\frac{1}{u}+\frac{1}{f}=\frac{1}{-50}+\frac{1}{25}=\frac{1}{50}\Rightarrow v=50\; cm

Magnification is

m=\frac{v}{u}=-\frac{50}{50}=-1

Therefore, the image would have been formed ate 50 cm from the pole and 0.5 cm below the principal axis. Thus, with respect to the X-axis passing through the edge of the cut lens, the coordinates of the image are (50\; cm, -1 \; cm).

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