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# Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is50cm−20cm−25cm−50cm

A
25cm
B
50cm
C
20cm
D
50cm
Solution
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#### Here the light passes through three refracting media, I, II \& III as shown in the figure.Media I \& II has a refractive index 1.5 and radius of curvature 20cm. While medium II has a refractive index of 1.7 and it acts as a concave lens.Let the focal length of the three media be f1,f2,f3.Applying the lens makers formula1f=(μ−1)(1R1−1R2)For media I,R1=∞ since it is a plano convex lens.1f1=(1.5−1)(1∞−1−20)=0.5×120=140For media II,1f2=(1.7−1)(1−20−120)=0.7×(−220)=−0.710For media III,Since media I & III are similar we can write1f3=140For applying the formula for equivalents lenses,1feq=1f1+1f2+1f3⇒1feq=140−0.710+140⇒1feq=1−2.8+140=−0.840=−150∴feq=−50cmHence the correct answer is option (D).

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