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CBSE Class 10 Science 2016 Term II Outside Delhi Set 3

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Question : 10 of 11
Marks: +1, -0
The image formed by a spherical mirror is real, inverted and is of magnification - 2 . If the image is at a distance of 30cm30 \mathrm{cm} from the mirror, where is the object placed ? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10cm10 \mathrm{cm} towards the mirror.
Solution:  
Given, m=−2,v=−30cmm=-2, v=-30 \mathrm{cm}
We know that,
m  =  −vum\;=\;\frac{-v}{u}
−2  =  30u-2\;=\;\frac{30}{u}
u  =−15cmu\;=-15 \mathrm{cm}
Now,
f=  uvu+v=  −15×−30−15−30=  450−45=−10cmf=\;\frac{u v}{u+v}=\;\frac{-15 \times -30}{-15-30}=\;\frac{450}{-45}=-10 \mathrm{cm}.
If the object is shifted 10cm10 \mathrm{cm} towards the mirror then, u=−5cmu=-5 \mathrm{cm}, i.e., object is between pole and focus, thus image formed will be virtual, erect and magnified.
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