Derive the formula `(1)/(v)-(1)/(u)=(1)/(f)` for a thin convex v u f 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 meaning] 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

Consider the ray diagram given as below

In the above figure triangle A.B.O and ABO are simnilar such that
`(A.B.)/(AB)=(OB.)/(OB)`
From eqs (i) and (ii) we get
`(OB)/(OB) =(FB)/(OF)=(OB.-OF)/(OF)`
Dividing both sides by uvf we get
`(1)/(f)=(1)/(v )-(1)/(u)`
this is the required thin lens formula for real image formed by convex lens
for a plano convex lens `R_(1) =+0.20 m ` and `R_(2) =-infty` here `mu =1.5`

Using lens maker .s formula
`=(1.5-1) ((1)/(+0.20)+(1)/(infty))`
`=0.5 xx(1)/(0.20)`
`rarr f=+0.4 m`