Question

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 materials refractive indices `mu_(1)` and `mu_(2)` and R is the radius curvature of the curved surface of the lenses, the focal length of the combination is
A. `(R )/(2(mu_(1) + mu_(2)))`
B. `(R )/(2(mu_(1) - mu_(2)))`
C. `(R )/((mu_(1) - mu_(2)))`
D. `(2R)/((mu_(2) - mu_(1)))`

Answer 1

Correct Answer - C
Focal length of the combination,
`(1)/(f)=(1)/(f_(1))+(1)/(f_(2))` ….(i)
We have, `(1)/(f_(1))=(mu_(1)-1)((1)/(oo)-(1)/(-R))=(mu_(1)-1)/(R )`
and `(1)/(f_(2))=(mu_(2)-1)((1)/(-R)-(1)/(oo))=-((mu_(2)-1))/(R )`
Putting these values of `(1)/(f_(1))` and `(1)/(f_(2))` in Eq. (i)
`(1)/(f)=((mu_(1)-1))/(R )-((mu_(2)-1))/(R )=([mu_(1)-1-mu_(2)-1])/(R )=(mu_(1)-mu_(2))/(R )`
`f=(R )/(mu_(1)-mu_(2))`