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A bi-convex lens is formed with two thin...

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 if 1.2 Both the curved surfaces are of the same radius of curvature `R=14cm. ` For this bi-convex lens, for an object distance of 40cm, the image distance will be

A

`-280.0 cm`

B

`40.0cm`

C

`21.5 cm`

D

`13.3 cm`

Text Solution

Verified by Experts

The correct Answer is:
B
According to lens maker's formula
`1/f = (n-1)((1)/(R_(1)) - 1/(R_(2)))`
For the first lens,
`n = 1.5, R_(1) = +14 cm, R_(2) = oo`
`:. 1/(f_(1)) = (1.5-1) ( 1/14 - 1/(oo)) = (0.5)/(14)`
For the second lens, `n = 1.2, R_(1) = oo , R_(2) = - 14 cm`
`:. (1)/(f_(2)) = (1.2-1) (1/oo - 1/(-14)) = (0.2)/(14)`
The focal length of the bi-convex lens is
`1/f = (1)/(f_(1)) + 1/(f_(2)) = (0.5)/(14) + (0.2)/(14) = (0.7)/(14) = (1)/(20)`
According to thin lens formula, `1/v - 1/u = 1/f`
Here, `u = - 40 cm, f = 20 cm`
`:. 1/v - (1)/(-40) = (1)/(20)` or `(1)/(v) = (1)/(20) - (1)/(40)` or `v = 40 cm`
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