A thin concave lens and a thin convex lens are kept in contact. The ratio of magnitudes of powers of the two lenses is 2323 and focal length of the combination is 30 cm. The focal length of individual lenses are Only one correct answerA.–15 cm, 10 cmB.–75 cm, 50 cmC.75 cm, –50 cmD.75 cm, 50 cm
Question
A thin concave lens and a thin convex lens are kept in contact. The ratio of magnitudes of powers of the two lenses is 2323 and focal length of the combination is 30 cm. The focal length of individual lenses are Only one correct answerA.–15 cm, 10 cmB.–75 cm, 50 cmC.75 cm, –50 cmD.75 cm, 50 cm
Solution
The power of a lens is the reciprocal of its focal length (in meters). So, if P1 and P2 are the powers of the concave and convex lenses respectively, and f1 and f2 are their focal lengths, we have:
P1 = -1/f1 (since concave lens has negative power) P2 = 1/f2 (since convex lens has positive power)
Given that the ratio of the magnitudes of the powers of the two lenses is 23:23, we have:
|P1|/|P2| = 23/23 = 1
So, |f2| = |f1|
Also, when the lenses are in contact, the focal length F of the combination is given by:
1/F = 1/f1 + 1/f2
Substituting F = 30 cm = 0.3 m, f2 = -f1 (since f1 and f2 have same magnitudes but opposite signs), we get:
1/0.3 = 2/f1
Solving this, we get f1 = -0.
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