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.

Options

A. `{:(P,Q,R,S),(1,2,3,4):}`
B. `{:(P,Q,R,S),(2,4,3,1):}`
C. `{:(P,Q,R,S),(4,1,2,3):}`
D. `{:(P,Q,R,S),(2,1,3,4):}`

Answer

B

Explanation

First of all let us calculate focal length of double convex lens.
`(1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f)=(1.5-1)((1)/(+r)-(1)/(-r))=0.5xx(2)/(r)`
`rArr" "f=r`
P: Two convex lens are put in contact so effective focal length `(1)/(f.)=(1)/(r)+(1)/(r)rArrf.=r//2`. Hence, option (2) is correct.
Q: Focal length of plano-convex lens becomes 2r but two such lenses in contact produce effective focal length r. Hence, option (4) is correct.
Without going further you can see that only option (b) is matching for the two cases and hence this has to be the answer but let us proceed further.
R: Two plano-concave lenses in contact are same as one double concave lens whose focal length will be -r same as that of convex but of opposite sign. Hence, option (3) is correct.
`(1)/(f)=(1)/(r)+(1)/(-2r)rArrf=2r` hence, option (1) is correct.
`P-2, Q-4, R-3, S-1` is correct.
Hence, option (b) is correct.