A plano - convex lens has a focal length of 0.25 m and is made of glass of refractive index 1.5. Find the radius of curvature of its curved surface. If two such lenses are placed with their curved surfaces in contact then what will be the focal length of the combination? If the space between them is filled with a liquid of refractive index 1.7, what will be the focal length of the combination?

Explanation

Given `r=?, f=0.25m, n=1.5, n_(1)=1.7`
For a plano convex lens,

(i) `(1)/(f)=(n-1)((1)/(oo)+(1)/(r))`
`(1)/(0.25)=(1.5-1)((1)/(r))`
hence `r=0.5xx0.25=0.125m`
`r=0.125m`
(ii) When thin lenses are in contact,
`(1)/(f)=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3))`
where, `(1)/(f_(3))=(n_(1)-1)((1)/(-r_(1))+(1)/(-r_(2)))`
i.e., `(1)/(f_(3))=(1.7-1)((-2)/(0.125))=(-1.4)/(0.125)`
hence, `(1)/(f)=(1)/(0.25)+(1)/(0.25)+(-1.4)/(0.125)=(1+1-2.8)/(0.25)`
i.e., `(1)/(f)=(0.8)/(0.25)`
`therefore` Focal length of the combination `=(0.25)/(-0.8)= -0.3125m`.