CBSE Class 10 Science 2019 Outside Delhi Set 2

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Question : 5
Total: 11
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=+5D
We have,
‌ Power, ‌P‌=‌
1
f(‌ in meter ‌)

+5‌=‌
1
f

f‌=‌
1
5
m

‌=‌
100
5
=20‌cm

Focal length, f=20‌cm(or+20‌cm ).
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=−1
Also,
m‌=‌
v
u

v‌=−u
From the lens formula,
‌
1
v
−‌
1
u
=‌
1
f

−‌
1
u
+‌
1
u
‌
=‌
1
f

‌
−2
u
‌
=‌
1
f

u‌=−2f
u‌=−2×20‌‌[∵f=20‌cm]
‌=−40‌cm.
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