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CBSE Class 10 Science 2023 Outside Delhi Set 2

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Question : 4 of 12
Marks: +1, -0
To obtain a magnification of +2 with a concave mirror of radius of curvature 60 cm60\text{ cm} the object distance must be
Solution:  
Given: The magnification +2.0 of a concave mirror of radius of curvature 60.0  cm\text{ cm}.
Focal length =  602=−30=\;\frac{60}{2}=-30
(-ve is taken because the focus of the mirror is behind the pole.)
Magnification, m=  −vum=\;\frac{-v}{u}
Putting the value of magnification in the above formula we get,
  −vu  =2\;\frac{-v}{u}\;=2
v  =−2uv\;=-2 u
vv is image distance, uu is object distance and ff is focal length.
Since,
  1u+  1v=  1f\;\frac{1}{u}+\;\frac{1}{v}=\;\frac{1}{f}
Putting the values
  1u+  1−2u  =  1−30\;\frac{1}{u}+\;\frac{1}{-2u}\;=\;\frac{1}{-30}
  12u  =  1−30\;\frac{1}{2u}\;=\;\frac{1}{-30}
u  =−  302 cmu\;=-\;\frac{30}{2}\text{ cm}
u  =−15 cmu\;=-15\text{ cm}
Hence, the object distance is −15 cm-15\text{ cm}.
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