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CBSE Class 10 Science 2019 Outside Delhi Set 2

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Question : 5 of 11
Marks: +1, -0
The power of a lens in +5 diopters. What is the nature and focal length of this lens ? At what distance from this lens should an object be placed so as to get its inverted image of the same size?
Solution:  
Given, P=+5DP=+5 D
We have,
   Power,   P  =  1f(   in meter   )\; \text{ Power, } \; P\;=\;\frac{1}{f(\; \text{ in meter } \;)}
+5  =  1f+5\;=\;\frac{1}{f}
f  =  15 mf\;=\;\frac{1}{5} \text{ m}
  =  1005=20 cm\;=\;\frac{100}{5}=20 \text{ cm}
Focal length, f=20 cm(or+20 cmf=20 \text{ cm} (or +20 \text{ cm} ).
Since, focal length of the lens is positive.
Therefore, the nature of lens is convex.
Same size and inverted image is formed when
Magnification, m=−1m=-1
Also,
m  =  vum\;=\;\frac{v}{u}
v  =−uv\;=-u
From the lens formula,
  1v−  1u=  1f\;\frac{1}{v}-\;\frac{1}{u}=\;\frac{1}{f}
−  1u+  1u  =  1f-\;\frac{1}{u}+\;\frac{1}{u}\;=\;\frac{1}{f}
  −2u  =  1f\;\frac{-2}{u}\;=\;\frac{1}{f}
u  =−2fu\;=-2 f
u  =−2×20    [∵f=20 cm]u\;=-2 \times 20 \;\; [ \because f=20 \text{ cm} ]
  =−40 cm.\;=-40 \text{ cm} .
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