A 5cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 15 cm. Find the nature, position, size of the image and it magnification
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Answer: The size of the image is 10 cm and the image is real and inverted.
Explanation:
Given that,
Height of object h = 5 cm
Focal length f = 20 cm
The distance of the object u = -30 cm
Using lens's formula
\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}
f
1
=
v
1
−
u
1
\dfrac{1}{20}=\dfrac{1}{v}-\dfrac{1}{-30}
20
1
=
v
1
−
−30
1
\dfrac{1}{v}=\dfrac{1}{60}
v
1
=
60
1
v = 60v=60
The image is formed at 60 cm on the other side from the lens.
The magnification is
m = \dfrac{v}{u}m=
u
v
m = \dfrac{60}{-30}m=
−30
60
m = -2m=−2
The image is real, inverted .
Size of the image,
m = \dfrac{h'}{h}m=
h
h
′
-2 = \dfrac{h'}{5}−2=
5
h
′
h' = -10 cmh
′
=−10cm
Hence, The size of the image is 10 cm and the image is real and inverted.
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