A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different material of refractive indices `mu_(1)` and `mu_(2)` and R is the radius of curvature of the curved surface of the lenses, then focal length of the combination is

Options

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

Answer

c

Explanation

Focal length of combination
`(1)/(f)=(1)/(f_(1))+(1)/(f_(2))`
Using lens maker’s formula
`(1)/(f_(2))=(mu_(2)-1)((1)/(-R)-(1)/(oo))=-((mu_(2)-1))/(R )`
`(1)/(f_(1))=(mu_(1)-1)((1)/(oo)-(1)/(-R))=(mu_(1)-1)/(R )`
or `(1)/(f_(1))=((mu-1))/(R )`
`(1)/(f_(2))=-((mu_(2)-1))/(R )`

Putting these values in Eq (i), we get
`rArr(1)/(f)=((mu_(1)-1))/(R )-((mu_(2)-1))/(R )`
`rArr(1)/(f)=((mu_(1)-1-mu_(2)+1))/(R )`
`rArr(1)/(f)=(mu_(1)-mu_(2))/(R )`
`f=(R )/((mu_(1)-mu_(2))`