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
B
1.2cm
C
1.4cm
D
0.8cm

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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