Question

derivation of lens makers formula

Answer 1

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.

Answer 2

For a spherical lens: 1/s1+n/s1' = (n-1)/(R1) where: 1 = index of refraction of air n = index of refraction of lens s1 = distance to object s1' = distance to image R1 = radius of curvature of the lens and applying this to the other side of the lens: -n/s1'+1/s2' = (1-n)/R2 = -(n-1)/R2 with s2' = distance to final image R2 = radius of curvature of other side of lens adding these two equations: 1/s1+n/s1' + -n/s1'+1/s2' = 1/s1+1/s2' 1/s1+1/s2' = (n-1)/R1 - (n-1)/R2 = (n-1)[1/R1-1/R2] and the thins lens equation gives 1/s+1/s'=1/f where f is the focal length and substituting this gives the lens maker equation 1/f = (n-1)[1/R1-1/R2]