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Question:

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 :-280.0 cm. 40.0 cm. 21.5 cm 13.3 cm.

-280.0 cm.

13.3 cm.

21.5 cm

40.0 cm.

Solution:

Applying lens maker formula for lens 1,
1/f1 = (μ-1)(1/R1 - 1/R2)
1/f1 = (1.5-1)(1/14 - 0)
1/f1 = 0.5/14
For lens 2,
1/f2 = (μ-1)(1/R1 - 1/R2)
1/f2 = (1.2-1)(0 - (1/14))
1/f2 = 0.2/14
Now,
1/f = 1/f1 + 1/f2
so 1/f = 0.7/14
Therefore, From lens formula :
1/v = 1/f + 1/u
1/v = 7/140 + 1/40
v = 40cm