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

(c ) given, `P_(1)+P_(2)=9`
We have,
`P=P_(1)+P_(2)-dP_(1)P_(2)`
`rArr 27/5=9-20/100xxP_(1)P_(2)`
Again `(P_(2)-P_(1))^(2)=(P_(1)+P_(2))^(2)-4P_(1)P_(2)`
`rArr P_(2)-P_(1)=3`
On solving Eqs. (i) and (ii), we get
`P_(1)=3and P_(2)=6`