The age-old question, "Why is the reflection on your glasses green in a selfie?". Seriously though it did catch my attention when receiving a Snapchat from a friend who wears glasses. The reflection on their glasses was green, yet I could see that their screen wasn't green - since it's a selfie and uses the front-facing camera.

This is interesting so I’m taking a small trip back to some Physics I learned in high school to explain the green reflection.

The reflection is caused by the anti-reflective coating on the glasses which is in place to reduce the glare. Let's figure out how thick the coating on my friend's glasses is, approximately. We'll assume magnesium fluoride (refractive index, n = 1.38) is used as the anti-reflective coating and that the wavelength of the reflected light is 541 nanometres.

When the light ray meets the coating it is partly reflected and partly transmitted, this happens again when the originally transmitted light reflects off of the glass. Since the glass has a higher refractive index (approximately 1.52) than the coating there is no phase change and therefore the phase difference is due to the optical path length distance only.

From the diagram we can see that,

$$Path\ Difference = 2n_{film}d$$

To reduce the overall reflection and maximise the transmission we need to make these two reflected rays interfere destructively i.e. peak meets trough. The minimum distance that this happens at is when the path difference is equal to half of the wavelength. The minimum distance is used as some would consider it wasteful to put 40m of anti-reflective coating on glasses.

$$2n_{film}d= \frac{\lambda}{2}$$

This can be rearranged to form an equation that can finally answer our question, how thick is the coating?

$$d= \frac{\lambda}{4n_{film}}$$ $$= \frac{541\times10^{-9}}{4\times1.38}$$ $$= 9.80\times10^{-8}m \ (\approx 0.1\mu m)$$