Two thin lenses have a combined power of +9 D.When they are sparated by a distance of 20 cm.
Their equivalent power becomes`+(27)/(5)D`.Their individual powers (in diopters)are

Options

A. `1,8`
B. `2,7`
C. `3,6`
D. `4,5`

Answer

C

Explanation

When two thin lenses of powders `P_(1)` and `P_(2)` are held in contact with each other,the power of the combination is given by
`P=P_(1)+P_(2)`
`therefore 9=P_(1)+P_(2)`
When two thin lenses of power `P_(1)` and `P_(2)` are separated by a distance d,the equivalent power is given by
`P+P_(1)+P_(2)-dP_(1)P_(2)`
`therefore(27)/(5)=P_(1)+P_(2)-(20)/(100)P_(1)P_(2)`
`(27)/(5)=9-(20)/(100)P_(1)P_(2)`......(Using (i))
`P_(1)P_(2)=18`
On solving (i) and (ii) ,we get
`P_(1)`=3D,`P_(2)`=6D