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).

Options

A. `6.67`
B. `-6.67`
C. `33.3`
D. `20`

Answer

A

Explanation

`(1)/(v)-(1)/(v)=(1)/(f) implies (1)/((d-u))-(1)/((-u))=(1)/(f)`
`impliesu^(2)-du+df=0 implies d=(u^(2))/((f-u))`
for minimum `d,u=-2f` Hence, `d_(min.)=4f`