A convex lens of focal length 30 cm is placed in contact with a...

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ________

Options

A30
B45
C $\frac{60}{7}$
D15

Correct answer

D. 15

Step-by-step solution

Equivalent focal length

\begin{aligned}<br/>& \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2} \\ & =\frac{1}{30}+\frac{1}{-20}=\frac{2-3}{60}=-\frac{1}{60} \\ & f=-60 \mathrm{~cm}<br/>\end{aligned}

Lens formula

\begin{aligned}<br/>& \frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\ & \frac{1}{\mathrm{v}}-\frac{1}{-20}=\frac{1}{-60} \\ & \mathrm{v}=-15 \mathrm{~cm}<br/>\end{aligned}

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