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Question

An object of height $$4$$ cm is placed at a distance of $$15 cm$$ in front of a concave lens of power, $$-10$$ dioptres. Find the size of the image.


A
1.6cm
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B
1.2cm
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C
1.4cm
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D
0.8cm
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Solution

The correct option is A $$1.6 cm$$
$$h_0=4 cm$$
$$u=-15 cm$$
$$P=-10\ D\Rightarrow f=\dfrac {-1}{10}m$$
We know: $$\dfrac {1}{f}=\dfrac {1}{V}-\dfrac {1}{u}$$
So, $$-10=\dfrac {1}{V}+\dfrac {1}{0.15}$$
or, $$\dfrac {1}{V}=-\dfrac {10}{1}-\dfrac {1}{0.15}=-\dfrac {1.5-1}{0.15}$$
or, $$\dfrac {1}{V}=\dfrac {-2.5}{0.15}$$
or, $$V=\dfrac {-0.15}{2.5}m$$
So, $$m=\dfrac {v}{u}=\dfrac {-0.15}{2.5\times -15}$$ $$=\dfrac {1}{250}m=0.4\ cm$$
or, $$\dfrac {h_i}{4}=0.4\ cm$$
or, $$h_1=1.6\ cm$$

Physics

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