A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different location separated by 20 cm. Determine the focal length of the lens.
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Answer:
f=21.4cm
Explanation:
The image of the object can be located on the screen for two-position of convex lens such that u and v are exchanged.
The separation between two positions of the lens is, d= 20 cm
From the figure,
u1+v1=90cm
v1−u1=20cm
Solving,
v1=55cm,
u1=35cm
From lens formula,
1/v − 1/u = 1/f
1/55 - 1/(-35) = 1/f
1/f = (1/55) + (1/35)
1/f = (55×35)/90
⇒f=21.4cm
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