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# 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 :converging lens of focal length 50 cm.diverging lens of focal length 15 cmdiverging lens of focal length 50 cmconverging lens of focal length 15 cm

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
Solution
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#### Ths is a combination of convex, concave and convex lens. Number them 1,2,3 given f1=f3=20 cmμ1=μ3=1.5μ2=4/3μ2=4/3 Now densmaker formula 1f=(μr−1)(1R1−1R2) for (1) 1f1=(1.5−1)(1R1−(−1R)) (equi convex lenS R1=R2)120=12×2RR=20 cm for (2) 1f2=(43−1)(1R1−1R2)1f2=13(−2R)f2=−30 cm Now we know that ieffective =P1+P2+P31feq=120−130+120feq =15 cm So it is a converging lens of focal length 15 cm.

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