## Friday, December 21, 2018

### Selected Questions-Answers From All Experts Astronomy Forum (Chromatic Aberration)

Question:  I am considering getting a refracting telescope and would like to know more about chromatic aberration. What exactly is it and how would it affect a lens?-  Bill, Montreal

Answer:  Chromatic aberration is just a result of dispersion of light rays entering the objective lens such that not all rays meet at the focus as they should.    Reference to the diagram-sketch shown below will help to explain this aberration, compared to how the rays ought to behave:

Here, the top image shows the effect of chromatic aberration with different rays directed to different locations.  The bottom image shows how the rays ought to behave, i.e. in meeting at one focus.   The source of the aberration is hinted in the name of it "chroma" for color, or wavelength. In this case, we note the component colors of white light possess slightly different wavelengths, i.e. red is longer than yellow, yellow is longer than blue and so on.

Because of the differing wavelengths ( l1,  l2 ..  ) we expect the light to be refracted by different amounts on entering an uncorrected lens.  This is because the index of refraction is given by:

n  =  c / v

where c is the speed of light and v is the speed through the medium (e.g. glass).  But c  =  f l   so  if  l  changes then n must too.   Hence, the light rays are refracted (bent) by differing amounts.  In this case, the shorter wavelengths are bent the most  while longer (e.g. red) wavelengths are bent the least.  It can be shown, for example, that a ratio of refractive indices, say n1 and n2 can be expressed:

l1 /   l2  =  ( c/ n1) /  (c/ n2)  =   n2 /  n1

Taking into account the two angles: Θ1 = angle of incidence, and Θ2 = angle of refraction, we may write:

n1 sin Θ1 = n2 sin Θ2   or    l2  sin Θ1 =    l1 sin Θ2

Or:    l1 /   l2  =  sin Θ2  /   sin Θ1

For blue light to bend more, means that for such a ray, Θ2   is greater than Θ2  for red light.    (Assuming the same angles of incidence  Θ1)  It is an instructive exercise to use the preceding relations to show this is true.  For example, taking a blue wavelength of 400 nm, vs. a red of 700 nm, and taking the same angle of incidence, say Θ1 =   45 deg.

The disparity between focal points accounts for  chromatic aberration, the effect of which is to produce color fringes around an image.

The correction of this aberration is done by the construction of a 2-element lens which is called an achromatic objective. Hence, when purchasing a refracting telescope this is an attribute you want to look for.   The lower diagram shows how the achromatic objective corrects for the disparity between focal points.

For this objective one element is concave the other is convex. In addition, one is made of crown glass the other of flint glass so each has a different index of refraction to correct for the unwanted difference of refraction from the chromatic aberration.  The concave element causes incoming light ways to diverge but only enough to correct for the unwanted aberration.

The lens combination still permits the overall convergence of the incident light to a single focus.   One final point is worth mention: the achromatic objectives designed for visual range observation (such as for astronomical telescopes) are corrected only for the green-yellow region of the visible spectrum.  That is because this region is the one to which the human eye has greatest sensitivity.