Can mirrors give rise to chromatic aberration?

Chromatic aberration is a type of image defect due to the fact that different wavelengths of light have different refractive indices. In almost all sources I read so far, this type of optical aberration is discussed only with respect to lenses.

The following text is from this webpage:

For many years, chromatic abberation was a sufficiently serious problem for lenses that scientists tried to find ways of reducing the number of lenses in scientific instruments, or even eliminating them all together. For instance, Isaac Newton developed a type of telescope, now called the Newtonian telescope, which uses a mirror instead of a lens to collect light.

The above statement hints that chromatic aberration is not present in mirrors due to their extensive usage in place of lenses long time ago. But, is the chromatic aberration eliminated completely or partially due to the use of mirrors? I'm having this doubt since, refraction takes place even in mirrors in addition to reflection, from the glass layer (present before the silvered surface). Or in other words, can mirrors give rise to chromatic aberration?

• I think you mix normal bathroom mirrors with telescope mirrors. The former ones have the glas in front to protect the reflective coating while in the latter one the ground plate is on the back side. – Hartmut Braun Dec 28 '19 at 11:54
• @HartmutBraun, Thanks for the comment. So, telescope mirrors do not have glass layer to protect the silvered surface? Further, do ordinary bathroom mirrors (let it be convex, concave, plane or anything else) exhibit chromatic aberration due to refraction from the glass layer? – Guru Vishnu Dec 28 '19 at 11:59
• telescope mirrors are re-coated regularly. No, as far as I can tell there is no protection on top of the reflective coating. On bathroom mirrors you can sometimes see rainbow effects when the lighting conditions are right. Here the answer is: yes – Hartmut Braun Dec 28 '19 at 12:03

2 Answers

Reflecting light from a back-surface glass mirror is equivalent to passing the light through a glass plate of twice the thickness of the mirror glass (because light reflecting from a back-surface glass mirror has to pass through the glass in both directions).

A very thin light beam passing through a flat glass plate at an angle will be refracted in one direction as it enters the glass, then will be refracted in the other direction as it exits the glass, so the portions of the beam outside the glass will be parallel, but slightly offset from each other.

Because the refractive index of glass is wavelength dependent, the amount of offset will be slightly different for beams with different wavelengths. That means the red component of a reflected image will be slightly offset from the blue component, for example. So, the reflection of, e.g., a white cube at a shallow angle will have a slight rainbow effect on its edges.

A front-surface mirror does not have that problem.

• Thank you for your answer. By "a shallow angle" do you mean the angle of incidence is close to $90^\circ$? – Guru Vishnu Dec 29 '19 at 4:20
• By "shallow angle", I mean the angles of incidence and reflection are greater than 45 degrees away from normal (away from perpendicular to the surface). But of course there will be a slight offset at any angle of incidence greater than 0 degrees away from normal; there will simply be a greater offset at greater angles of incidence. And, greater glass thickness produces greater offset. – S. McGrew Dec 29 '19 at 4:38

The reflection efficiency of a mirror may be wavelength-dependent, but the angle through which the light is reflected is not. Astronomical mirrors are "first surface" mirrors; there is no protective (and potentially refractive) coating.

So no chromatic aberration.