Four combinations of two thin lenses are given in List `I`. The radius of curvature of all curved surfaces is `r` and the refractive index of all the lenses is `1.5` Match lens combinations in List `I` with their focal length in List `II` and select the correct answer using the code given below the lists.
(A) `(p) 2 r`
(B) `(q) ( r)/(2)`
( C) `(r) - r`
(D) `(s) r`.
Code :

Options

A. `A-p,B-q,C-r,D-s`
B. `A-q,B-s,C-r,D-p`
C. `A-s,B-p,C-q,D-r`
D. `A-q,B-p,C-r,D-s`

Answer

B

Explanation

(A) `(1)/(f)=(mu - 1)((1)/( r) + (1)/( r)) = (1.5 - 1)((2)/( r)) = (1)/( r)`
`rArr f = r`
`(1)/(f')=(1)/(f_1)+(1)/(f_2) rArr f' = ( r)/(2)`
`A rarr q`
(B) `(1)/(f_1) = (1.5 - 1)((1)/(oo) + (1)/( r)) = (0.5)/( r)`
`rArr f_1 = 2 r = f_2`
`(1)/(f)=(1)/(f_1)+(1)/(f_2) rArr (1)/(f)=(1)/(2 r)+(1)/(2 r)`
`rArr f = r`
`B rarr s`
( C) `(1)/(f_1)=(1.5 - 1)((1)/(oo) - (1)/( r)) = -(0.5)/( r)`
`rArr f_1 = -2 r`
`(1)/(f_2) = (1.5 - 1)(-(1)/( r) - (1)/(oo)) = -(0.5)/( r)`
`rArr f_2 = -2 r`
`(1)/(f)=(1)/(f_1)+(1)/(f_2)= -(1)/(2 r) -(1)/(2 r)`
`f = -r`
`C rarr r`
(D) `(1)/(f_1)=(1.5 -1)((1)/( r) - (1)/(- r)) = 0.5 xx (2)/ (r ) = (1)/( r)`
`rArr f_1 = r`
`(1)/(f_2) = (1.5 - 1)((1)/(oo) - (1)/( r)) rArr (1)/(f_2) = -(0.5)/( r)`
`rArr f_2 = -2 r`
`(1)/(f)=(1)/(f_1)+(1)/(f_2)=(1)/( r) - (1)/(2 r) = (1)/( 2r)`
`rArr f = 2 r`
`D rarr p`
Thus option (b) is true.
(A) , (B) , ( C) , (D) .