Two thin lenses are kept coaxially in contact with each other and the focal length ofthe combination is 80 cm. If the focal length of one lens is 20 cm, the focal length ofthe other would be
Question
Two thin lenses are kept coaxially in contact with each other and the focal length ofthe combination is 80 cm. If the focal length of one lens is 20 cm, the focal length ofthe other would be
Solution
The focal length of a combination of lenses is given by the formula:
1/F = 1/f1 + 1/f2
where F is the focal length of the combination, and f1 and f2 are the focal lengths of the individual lenses.
In this case, we know that F = 80 cm and f1 = 20 cm. We want to find f2.
Substituting the known values into the formula, we get:
1/80 = 1/20 + 1/f2
To solve for f2, we first subtract 1/20 from both sides:
1/80 - 1/20 = 1/f2
This simplifies to:
1/80 - 4/80 = 1/f2
which further simplifies to:
-3/80 = 1/f2
Finally, we take the reciprocal of both sides to solve for f2:
f2 = -80/3 cm
So, the focal length of the other lens is -80/3 cm, or approximately -26.67 cm. This negative sign indicates that the lens is diverging.
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