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Question

A convex lens of focal length 20 cm is cut into 2 parts as shown in the figure. These two parts are placed at 30 cm and 50 cm on x-axis. A point object is placed at origin then for image formed by refraction from both lenses. Then,

x-coordinate of final image is 63.33 cm

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y-coordinate of final image is 1.33 cm

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final image is virtual

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final image is real

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Solution

The correct options are
A x-coordinate of final image is 63.33 cm
D final image is real
$\frac{1}{20} = \frac{1}{v_{1}} + \frac{1}{30} \to v_{1} = 60 c m \Rightarrow \frac{I_{1}}{2} = \frac{60}{- 30} \Rightarrow I_{1} = - 4 c m$

The image of the first lens acts as an object for the second lens. The object distance of the second lens is $60 - 20 = 40 c m$

$\frac{1}{20} = \frac{1}{v_{2}} - \frac{1}{40} \to v_{2} = 13.33 c m \Rightarrow \frac{I_{2}}{- 4} = \frac{13.33}{40} \Rightarrow I_{2} = - 1.33$

Hence the coordinates of the final image are,
$x \to 63.33 c m y \to - 3.33 c m$

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