IIT-JEE 2012 · Paper 1 · Physics Q10

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A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature $R=14$ cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be

Two thin plano-convex lenses placed with their flat faces together to form a bi-convex lens: the left one has n = 1.5 and the right one n = 1.2; both curved faces have R = 14 cm.

−280.0 cm.

40.0 cm.

21.5 cm.

13.3 cm.

Answer and worked solution

Official answer: B

Thin lenses in contact. Each plano-convex lens has $\frac1f=\frac{n-1}R$ :
$\frac1f=\frac{0.5}{14}+\frac{0.2}{14}=\frac{0.7}{14}=\frac1{20}\implies f=20\text{ cm}.$

Image. With $u=-40$ cm: $\frac1v=\frac1{20}-\frac1{40}=\frac1{40}$ , so $v=40$ cm.

(B)

Topics:Combination of lenses and mirrors Thin lenses and lens maker's formula

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IIT-JEE 2012 · Paper 1, Physics question 10