Refraction, Lenses, and Prisms

Seeing Things Normally, to see something you must see the light it reflects or the light it emits. So, how do you see something that is clear? Clear objects can be seen the light that passes through them being slightly bent. The amount of the bending is expressed as the refractive index.

The Invisible Man In the science fiction novel the Invisible Man, the title character creates a potion that changes his refractive index to match that of air. Today, we will recreate the effect.

Refraction Refraction occurs when light passes from one medium to another at an angle other than 90°. The direction of the beam is changed in proportion to the change in speed. This is quantified in Snell’s Law. Where θ 1 is the incident angle. θ 2 is the angle of refraction v 1 is speed of the wave in the first medium and v 2 its speed in the second. n 1 is the index of refraction of the first medium and n 2 that of the second.

Refraction When we view an object from a different medium, we see a virtual image of the object. The object may appear to be in a different place or to be bent.

Critical Angle Calculate θ 2 if the incident angle is 60° for a ray of light passing from air (n=1) to water (n=1.3). Calculate θ 2 if the incident angle is 60° for a ray of light passing from water (n=1.3) to air (n=1). At a certain critical angle, θ 2 becomes undefined. What happens at this angle? n 1 sinθ 1 = n 2 sinθ 2 (1)(0.87) = (1.3)sinθ 2 sinθ 2 = 0.67 θ 2 = 41.7° n 1 sinθ 1 = n 2 sinθ 2 (1.3)(0.87) = (1)sinθ 2 sinθ 2 = 1.22 arcsin(1.22) = undefined

Total Internal Reflection If the incident angle exceeds the critical angle, the wave cannot pass the interface. Instead it reflects off the interface as it would any reflective surface. This is what creates mirages on a hot day. TIR also has many useful applications.

Total Internal Reflection

Fiber Optics Traditional copper wires can only carry one signal at a time. Dozens of wires are bundled together to make a each cable, but the number of signals is still small. Fiber optic cables are individually thinner and each can carry multiple signals.

Fiber Optics If the ends of each strand are carefully arranged, a fiber optic cable can act as a camera. This has allowed the creation of endoscopes— tiny cameras on long, thin tubes that can be inserted into the body to allow doctors to examine a patient internally, without surgery.

SONAR All waves can undergo TIR. Ships use SONAR to detect obstacles and other ships. Military submarines can hide from SONAR using TIR caused by ocean layers with differing temperatures.