Two equi-convex lenses each of focal lengths 20 cm and refractive index 1.5 are placed in contact and space between them is filled with water of refractive index 4/3. The combination works as :
A
converging lens of focal length 50 cm.
B
diverging lens of focal length 15 cm
C
converging lens of focal length 15 cm
D
diverging lens of focal length 50 cm
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Updated on : 2022-09-05
Solution
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Correct option is C)
Ths is a combination of convex, concave and convex lens. Number them 1,2,3 given f1μ1μ2=f3=20cm=μ3=1.5=4/3
μ2=4/3 Now densmaker formula f1=(μr−1)(R11−R21) for (1) f11=(1.5−1)(R11−(−R1)) (equi convex lenS R1=R2)
201=21×R2R=20cm for (2) f21=(34−1)(R11−R21)f21=31(R−2)f2=−30cm
Now we know that ieffective feq1feq =15cm=P1+P2+P3=201−301+201 So it is a converging lens of focal length 15cm.
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