MAGNITUDE OF CHROMATIC ABERRATION

Calculating chromatic aberration:

when a lens is suffering with chromatic aberration the focal point is not a single but a multiple focal points are seen from violet to red colour on the principle axis of the lens

We use lens maker’s formula to measure longitudinal chromatic aberration.

  1/f = [ 𝝁 - 1][ 1/R1  - 1/R2  ] 

where f = focal length of given lens , R1 and R2  are radii of curvature of the given lens,

if the given lens suffers with chromatic aberration then the focal points are different for different colours. also the refractive indices are different.

let  the focal length of violet colour = fv

Focal length of red colour = fr 

and focal length of yellow colour = fy

1/fv = [ 𝝁v - 1][ 1/R1  - 1/R2  ] 

1/fr = [ 𝝁r - 1][ 1/R1  - 1/R2  ]  and 

also it is known that fv * fr = fy^2

1/fv - 1/fr = [ 𝝁v - 1][ 1/R1  - 1/R2  ] -  [ 𝝁r - 1][ 1/R1  - 1/R2  ] 

 

fr - fv /fr *fv  = [ 1/R1  - 1/R2  ] [𝝁v -𝝁r]

fr - fv / fy^2 = [ 1/R1  - 1/R2  ] [𝝁v -𝝁r]

fr - fv  = fy^2 * [ 1/R1  - 1/R2  ] [𝝁v -𝝁r]

multiply and divide by [𝝁y-1] ,where 𝝁y = refractive index of  yellow colour.

 fr - fv  = fy^2 * [ 1/R1  - 1/R2  ][𝝁v -𝝁r] [ 𝝁y-1] / [𝝁y-1]

we know that (𝝁v -𝝁r) / (𝝁y-1) = dispersive power of the lens,⍵.

hence

  fr - fv  = fy^2 * [ 1/R1  - 1/R2  ] [ 𝝁y-1] *⍵

 and 

[ 1/R1  - 1/R2  ] [𝝁y-1] = 1/ fy

therefore     fr - fv  = fy^2 *⍵ / fy

So, the magnitude of chromatic aberration is fr- fv = fy *⍵