Derive the formula `1/v -1/u =1/f` for a thin convex lens and use it to find the nature of the image for object distances less than the focal length.
[The symbols in the equation carry their usual meaningl]
A plano-convex lens has one surface flat and the other surface has radius of curvature 0.20 m. Its refractive index is 1.5. What is its focal length in air?

Explanation

For a. plano-convex lens, `R_(1) = infty` and `R_(2)=-0.20 cm`
Here, `mu = 1.5 cm`
Using lens maker.s formula,
`1/f =(mu-1) (1/R_(1)-1/R_(2))`
`=(1.5-1) (1/infty -1/(-0.20))`
`=0.5 xx 1/(0.20) (therefore 1/infty = 0)`
`rArr f = 0.4 m`