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

Options

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

Answer

C

Explanation

When two thin lenses of powers `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)`
`:.9=P_(1)+P_(2)` …(i)
When two thin lenses of power `P_(1)` and `P_(2)` are seprated by a distance d, the equivalent power is given by
`P=P_(1)+P_(2)-P_(1)P_(2)d`
`:. (27)/(5)=P_(1)+P_(2)-(20)/(100)P_(1)P_(2)implies(27)/(5)=9-(20)/(100)P_(1)P_(2)` (Using (i) )
`P_(1)P_(2)=18` ...(ii)
On solving (i) and (ii), we get
`P_(1)=3D. P_(2)=6D`