In this video we will show you how the focal length of a lens changes as the temperature changes and how the shift can be calculated.

Transcript Below

**Focal Length Changes with Temperature Concept**

In this video, we’re going to be talking about how the focal length can change for a lens as the temperature changes. The simplest idea is to have a thin lens. If you have a very thin lens that focuses light to a point, like coming from this direction, you’ll have the focal length, f.

Now that focal length will change with temperature. There will be two contributions. So, if we think of that focal length changing a particular amount called Δf that change in focal length Δf is equal to δ times f times ΔT.

**Focal length, Index of refraction, thermal expansion, and the coefficient of thermal defocus **

δ is the coefficient of thermal defocus, f is your focal length, and ΔT is your change in temperature.

Now if we take a closer look at δ is a combination of two or actually three material properties. So δ is defined as the thermal expansion coefficient of the lens material minus dn/dt where n is your c index of refraction. And that times one over n_{absolute} which is your index of refraction minus one.

So your dn/dT, your n, and your alpha [coefficient of thermal expansion] are all material properties. So thermal expansion coefficient [α] , dn/dT is the change in index of refraction with temperature, and this [1/(n_{abs} – 1)] is the refractive index.

This term looks very similar to the change in length of a material due to thermal expansion, which we’ll get into a little bit later [Next video].