Obtain the equation of thin lens.

Explanation

For refraction at two spherical surfaces of lens,
`(n_1)/(-u)+(n_1)/(v)=(n_2-n_1)[(1)/(R_1)-(1)/(R_2)]`
`therefore(1)/(-u)+(1)/(v)=((n_2)/(n_1)-1)[(1)/(R_1)-(1)/(R_2)]` [`therefore` Dividing by `n_1`]
`therefore(1)/(-u)+(1)/(v)=(n_(21)-1)[(1)/(R_1)-(1)/(R_2)]` ... (1)
and lens maker.s formula,
`1/f=(n_(21)-1)[(1)/(R_1)-(1)/(R_2)]` ... (2)
By comparing equation (1) and (2),
`1/f=(1)/(-u)+(1)/(v)` or `1/f=1/v-1/u`
Here, the distances are as per sign conventior and this equation is true for real and virtua images of convex and concave lenses.