Two similar thin equi-convex lenses, of focal f each, are kept coaxially in contact with each other such that the focal length of the combination is `F_(1)`, When the space between the two lens is filled with glycerin (which has the same refractive index `(mu=1.5)` as that of glass) then the equivalent focal length is `F_(2)`, The ratio `F_(1): F_(2)` will be

Options

A. `3: 4 `
B. `2 : 1 `
C. `1: 2 `
D. `2: 3 `

Answer

C

Explanation

`(1)/(f_(1)) = (1)/(f) + (1)/(f) = (2)/(f)`
`f_(1) = (f)/(2) = (R )/(2)`
`(1)/(f) = (1.5 - 1)` 2 /R
`= (1)/(2) xx (2)/(R ) = (1)/(R ) `
`(1)/(f_(2)) = (1)/(R ) - (1)/(R ) + (1)/(R ) = (1)/(R ) `
`f_(2) `= R
with glycerin : focal length of concave lens is formed
`(1)/(f.) = (m-1 ) (- (1)/(R ) - (1)/(R ) ) = (1)/(2) ( - (2)/(R ) ) = (-1)/(R )`
`(f_(1))/(f_(2)) = (R/ 2 )/(R) = (1)/(2)`