# Do convex lenses make parallel light rays of different wavelength converge to different points?

I'm starting to study cameras and lenses. By reading explanations and watching videos on convex lenses, I learnt that they make parallel light rays converge to a single point called the focal point.

Now, according to Snell's law, light of different wavelengths (such as different colours) is refracted by different angles. So it seems to me that different colours have different focal points.

• Related: What is chromatic aberration? and anything else tagged with chromatic-aberration. Easy once you know what it's called, very hard if you don't! Commented Dec 19, 2017 at 22:40
• Thank you for pointing it out. I will edit my question to make a different one. But I would like to leave the first question as a reminder at the end and your comment too. It could turn to be useful for others. Commented Dec 19, 2017 at 22:58

Do convex lenses make parallel light rays of different wavelength converge to different points?

Yes. The separation of different wavelengths of light is called dispersion. Different wavelengths of light refract at different angles because the refractive index of a transparent medium is frequency dependent. We often describe different materials, such as crown glass, flint glass, diamond, water, etc., as having "an" index of refraction, but that singular index is just representative of the refraction at a single wavelength. For instance, at Wikipedia's List of refractive indices, many of the materials' indices are specified at a wavelength of 589.29 nm.

Plot of refractive index vs. wavelength of various glasses. A material's dispersion is roughly the slope of the line through the refractive indices at the boundary of the shaded region (optical wavelength) for a particular material. By DrBob, from Wikimedia Commons. CC BY-SA 3.0

One quantification of the amount of dispersion in a particular refractive medium is called the Abbe number of that material. Roughly the Abbe number is the ratio of the material's refractive index in a particular yellow wavelength, to the difference between the refractive indices at particular blue and red wavelengths. The higher the Abbe number, the less dispersion a material exhibits.

Dispersion is what causes longitudinal chromatic aberration in lenses (see also, What is Chromatic Aberration?), such that different wavelengths of light are brought to focus at different focal lengths.

Diagram demonstrating longitudinal chromatic aberration, by DrBob from Wikimedia Commons. CC BY-SA 3.0

This is corrected by marrying two (or more) pieces of glass with different Abbe numbers. For instance, an achromatic doublet uses a crown glass convex element with a flint glass concave element to reduce the variation in the focal lengths of the optical light wavelengths.

Achromatic doublet correcting chromatic aberration, by DrBob from Wikimedia Commons. CC BY-SA 3.0

Other corrective elements exist, such as apochromats and superachromats.

• And, of course, another strategy is to dispense with lenses altogether; this is one of the reasons that high-end telescopes use mirrors. Commented Dec 20, 2017 at 18:53
• @Acccumulation Indeed. But it's really hard to get reflective optics in a package as small as a smartphone to take good selfies.
– scottbb
Commented Dec 20, 2017 at 18:59
• @scottbb Although, in an SLR lens, reflective optics do make smaller and lighter lenses than their refractive counterparts. They were quite popular in the 70s and into the 80s, but generally suffer from fixed apertures (no DOF control) and, arguably, unpleasing bokeh... unless you're into the whole swirly-doughnut-mess type of look for your backgrounds.
– J...
Commented Dec 21, 2017 at 14:23
• @Acccumulation if by "high end" you mean what professional astronomers use, the main limitation is not aberration, but aperture. Making a glass lens as big is hard, and it will bend under its own weight. (There are, of course, some exceptions). Chromatic aberration is not such a big problem in astronomy because most images are taken with filters. Of the most commonly used, the broad band are around 100 nm wide. Commented Dec 21, 2017 at 14:52

Light from a far distance object, like a star, arrive at the lens, as parallel rays. As they transverse the lens, they are forced to change their direction. They bend inward, we call this refraction from the Latin to bend backwards. We can draw a trace of these rays; they trace out the shape of a cone. What we find is, the apex of the violet cone of light forms closer to the lens then the green, yellow, orange, red etc., in other words images are formed downstream but each color at a different distance. Worst, the red projection distance being the greatest is larger than blue image. We can’t focus on but one color at a time. The other colors are therefor out of focus. We call this chromatic aberration (color error).

What I have just described is called longitudinal chromatic aberration. We can mitigate this by constructing a lens by sandwiching two lenses together, each with an opposite chromatic aberration. We use an achromatic doublet (English for without color error). A strong convex (positive power) lens combined with weak negative (concave). Additionally the glass used will be dissimilar for each. Such an arrangement brings the red and the violet apexes together. We are not finished.

We bring the red and violet together but their paths through the lens system still have different lengths so the focal lengths of each are a minuscule off (different). This is called transverse chromatic aberration. The result of this focal length difference, when we look at a star we see objects fringed by a rainbow of colors.

Now we go to work using several more lenses and we can mitigate but not expunge all the chromatic aberrations. However, a mirror lens, has its silvering on the outside of the glass. Light never need transverse the glass of a powerful objective (main lens). Thus they are free from chromatic aberrations.

Don’t think that’s it. All and all there are five more monochromic aberrations to deal with.

Yes, they do. This is the cause of chromatic aberration. It happens in two ways, actually. Axial chromatic aberration (also known as longitudinal CA) happens because different wavelengths focus at different distances. Transverse chromatic aberration ( or lateral CA) happens because the different wavelengths are magnified and distorted differently.

But, camera lenses are not simple lenses — they're complex combinations of different elements specifically designed to minimize this and other aberration (see What image-quality characteristics make a lens good or bad? for some other examples).

Look for lenses designated as achromatic or apochromatic as an indicator that the design particularly focuses on minimizing chromatic aberration — sometimes with lens names containing things like "APO".