Refraction in lenses
When a ray of light passes through a transparent object such as a block of glass, it refracts twice. Once when it enters the glass and once again when it exits. In order to trace the complete path a ray of light takes, both these points of refraction need to be considered separately. Failure to understand this makes it impossible to accurately predict the path light takes through transparent objects.
The illustration above shows the path a ray of light takes when moving through transparent objects of different shapes. At each interface, the line normal to the surface at that point can be shown by switching on the "Show Normal" option. The buttons at the bottom allow different shapes to be viewed.
The medium outside of the lenses has an optical density* of 1. The optical densities of the lenses are 1.5. As the light travels through the lenses, it refracts in accordance to Snell's law by refracting towards the normal as it enters the lens and then refracting away from the normal as it passes back out.
The behavior of the light rays is also consistent with moving through an object with an optical density of 1.5. If the light ray hits an interface from within the lens at an angle of incidence that exceeds the critical angle*, the light ray reflects off of the surface rather than passing through.
Try the Snell's Law - refraction practice problems to test your understanding of the calculations