A plano convex lens of refractive index `mu_(1)` and focal length `f_(1)` is kept in contact with another plano concave lens of refractive index `mu_(2)` and focal length `f_(2)`. If the radius of curvature of their spherical faces is R each and `f_(1)=2f_(2)`, then `mu_(1)` and `mu_(2)` are related as :

Options

A. `mu_(1)+mu_(2)=3`
B. `3mu_(2)-2mu_(1)=1`
C. `2mu_(2)-mu_(1)=1`
D. `2mu_(1)-mu_(2)=1`

Answer

D

Explanation

`1/(f_(1))=(mu_(1)-1)(1/R-1/(oo))`
`rArrf_(1)=R/(mu_(1)-1)`
`1/(f_(2))=(mu_(2)-1)(1/(oo)-1/R)=(1-mu_(2))/R`
`rArrf_(2)=R/(1-mu_(2))`
`abs(f_(1))=2abs(f_(2))rArrR/(mu_(1)-1)=(2R)/(mu_(2)-1)rArrmu_(2)-1=2mu_(1)-2rArr2mu_(1)-mu_(2)=1`