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Two planoconvex lenses each of the focal...

Two planoconvex lenses each of the focal length of`10cm`&refractive index`3//2`are placed as shwon .In the space left water`(R.I.=4//3)`is filled.Then whole arrangement is in air.The optical power of the system is(in diopters).

A

`6.67`

B

`-6.67`

C

`33.3`

D

`20`

Text Solution

Verified by Experts

The correct Answer is:
A
`(1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(10)=(1.5-1)((1)/(oo)-(1)/(-R)) rArr (1)/(10)=(0.5)/(R ) rArr R=5cm`
focal length of middle lense
`(1)/(f_(2))=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_(2))=((4)/(3)-1)((1)/(-5)-(1)/(5))`
`(1)/(f_(2))=(1)/(3)xx(-2)/(5)`
`(1)/(f_(2))=(-2)/(15)`
`(1)/(f_(eq))=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3)) rArr (1)/(f_(eq))=(1)/(10)-(2)/(15)+(1)/(10)`
`(1)/(f_(eq))=(3-4+3)/(30) rArr (1)/(f_(eq))=(1)/(15)`
for combination,`P_(eq)=(100)/(f_(eq))`
`P_(eq)=(100)/(15)D rArr P_(eq)=6.67D`
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