## Answers

**The lens maker’s derivation assumes some condition, they are**:

Thin lens is used for measure the distance from surface poles to lens optical centre distance.

Small aperture is taken.Consider the point object.Small angles are made by incident and refracted ray.Take convex lens with absolute refractive index in rarer medium. Thesurface P has refraction of a point. From distance V1, the image is produced.The distance values are 1I = V1, 1O = u and 12 = R1.During convex spherical surface, the refraction is

`(n_(1))/(-u)` + `(n_(2))/(V_(1))` = `(n_(2)-n_(1))/(R_(1))` ——(1)

The second ray is emerged along OI. The distance is n = V1.The lens maker’s derive the refractive index of lens.The second surface curvature radius is R2 and derive the following equation:

`(-n_(2))/(V_(1))` + `(n_(1))/(V)` = `(n_(1)-n_(2))/(R_(2))`= `(n_(2)-n_(1))/(-R_(2))` ——(2).

`(-n_(1))/(-n)` + `(n_(1))/(V)` = (`n_(2)` – `n_(1)` ) (`(1)/(R_(1))` – `(1)/(R_(2))` )

If R1 and R2are the radius of curvature of first and second refracting surfaces of athin lens of focal length f, then lens maker’s formula is `(1)/(f)` = (`n_(2)` -1) (`(1)/(R_(1))` – `(1)/(R_(2))` )

= (n -1) (`(1)/(R_(1))` – `(1)/(R_(2))` )

Where n is refractive index of material of lens with respect tosurroundings medium. If a lens separates two media of refractive indicesn1 and n3 then its focal length ‘f’ is

`(n_(3))/(f)` = `(n_(2)-n_(1))/(R_(1))` – `(n_(3)-n_(2))/(R_(2))` .

The lens maker’s formula is one step calculation. It is based onrefraction radius and length. Lens power is calculated by human eyecapacity and refractive power is suspended. The surface should be inplane.