A converging lens of focal length 200 cm is placed parallel to x-y plane such that the principal axis is along z-axis. The optical centre of the lens is at P(0, 0, 150 cm). Consider two points A(1cm, 2cm, 0) and B(2cm, 2cm, 0). The image of O, A and B is formed at O’ A’ and B’.

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A converging lens of focal length 200 cm is placed parallel to x-y plane such that the principal axis is along z-axis. The optical centre of the lens is at P(0, 0, 150 cm). Consider two points A(1cm, 2cm, 0) and B(2cm, 2cm, 0). The image of O, A and B is formed at O’ A’ and B’.

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$\frac{Area of {ΔO}^{'} A^{'} B^{'}}{Area of △ OAB} = 16$

The length A' B '= 4 cm

Coordinates of B’ = (8cm, 8cm, -450 cm)

Coordinates of A’=(4cm, 8cm, 0)

answer is B, C, D.

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Detailed Solution

$\begin{array}{l} m = \frac{f}{f + u} = \frac{200}{200 - 150} = 4 \\ \frac{x_{i}}{x_{0}} = \frac{y_{1}}{y_{0}} = 4 \\ v = - 600 cm, z_{i} = - 450 cm \end{array}$
$A' B' = 4 \times A B = 4 c m$