Ncert Exercises & Solutions

A thin convex lens of focal length 25cm is cut into two pieces 0.5cm 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.

Hint: Use the lens formula.

Step 1: Find the position of the object.

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

Step 2: Find the position of the image.

Applying lens formula, we have,
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$∴ \frac{1}{v} = \frac{1}{u} + \frac{1}{f} = \frac{1}{- 50} + \frac{1}{25} = \frac{1}{50}$
$∴ v = 50 cm$
Magnification is, m= $\frac{v}{u} = - \frac{50}{50} = - 1$
Thus, the image would have been formed at 50 cm from the optical centre and 0.5 cm below the principal axis. Hence, 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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