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ICSE Class 10 Physics 2018 Paper

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Question : 50 of 78
Marks: +1, -0
An object is placed at a distance of 12 cm12\ \text{cm} from a convex lens of focal length 8 cm8\ \text{cm}. Find:
(i) the position of the image
(ii) nature of the image
Solution:  
Given: u=12 cmu=12\ \text{cm} (negative), f=8 cmf=8\ \text{cm} (positive)
We know, by lens formulae,
    1f=  1v−  1u\;\;\frac{1}{f} = \;\frac{1}{v} - \;\frac{1}{u}
    1v=  1u+  1f\;\;\frac{1}{v} = \;\frac{1}{u} + \;\frac{1}{f}
or   1v=  1u+  1f\;\frac{1}{v} = \;\frac{1}{u} + \;\frac{1}{f}
or     1v=  1−12+  18\;\;\frac{1}{v} = \;\frac{1}{-12} + \;\frac{1}{8}
    1v=  −2+324=  124\;\;\frac{1}{v} = \;\frac{-2+3}{24} = \;\frac{1}{24}
∴    v=24 cm   (positive)   \therefore \;\; v=24\ \text{cm} \;\text{ (positive) }\;
Thus, the image is formed at a distance of 24 cm\text{cm} behind the lens.
We know,     m=  vu=  24−12=−2\;\; m = \;\frac{v}{u} = \;\frac{24}{-12} = -2
Thus, the image is Real, inverted and magnified in size.
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