Two thin lenses, when in contact, produce a combination of power`+10` diopters. When they are 0.25m apart, the power reduces to `+6`diopters. The focal lengths of the lenses are m and `"________________"` m

Options

A. 0.5 and 0.125
B. 0.5 and 0.75
C. 0.125.and 0.75
D. Botha have the same focal length 1.25

Answer

A

Explanation

(a) When lenses are in contact, then power
`P=1/f=1/(f_(1))+1/(f_(2))`
`10=1/(f_(1))+1/(f_(2))`….(i)
When they are placed a distance d apart
`P'=1/(F')=1/(f_(1))+1/(f_(2))-d/(f_(1)f_(2))`
`6=1/(f_(1))+1/(f_(2))-0.25/(f_(1)f_(2))...(ii)`
From Eqs. (i) and (ii), we get
`f_(1)f_(2)=1/16` ....(iii)
From Eqs. (i) and (iii), we get
`f_(1)+f_(2)=5/8`.....(iv)
Also, `(f_(1)-f_(2))^(2)=(f_(1)+f_(2))^(2)-4f_(1)f_(2)=(5/8)^(2)-4xx1/16=9/64`
`f_(1)-f_(2)=3/8`...(v)
On solving Eqs. (iv) and (v), we get
`f_(1)=0.5 m` and `f_(2)=0.125` m