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.

• A. (50 cm , -2 cm)
• B. (50 cm , -1 cm)
• C. (3 cm , -50 cm)
• D. (60 cm , -25 cm)

Answer 1

Answer: (B)

(50 cm , -1 cm)

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

Consider the image for this case.

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

Magnification, $m=\frac{v}{u}=\frac{-50}{50}=-1$

Thus the image would have been formed at 50 cm from the pole and 0.5cm below the principle axis.

Hence with respect to x- axis passing through the edge of the cut lens, the co-ordinates of the image are (50 cm, -1 cm)