Physics · Ch 9 — Optics
Applications of total internal reflection
Applications of total internal reflection
Total internal reflection (TIR) has several important everyday and technological applications, every one of them relying on light striking an interface at an angle beyond the critical angle.
OPTICAL FIBRE: an optical fibre consists of an extremely thin (only slightly thicker than a human hair), transparent, flexible CORE, surrounded by an optically RARER (lower refractive index), also-flexible CLADDING layer, the whole assembly wrapped for protection in an outer buffer and jacket; the entire fibre's thickness is under half a millimetre, and many such fibres can be bundled together inside one outer cover. A light signal (ray) entering the core undergoes repeated total internal reflections at the core-cladding boundary as it travels, and emerges after several kilometres with very low loss, moving at close to the highest possible speed attainable in that material (about 200,000 km/s in glass). The advantages of optical-fibre communication over conventional electrical/electronic communication include: broad bandwidth (a single fibre can carry over 90,000 independent TV channels simultaneously); immunity to electromagnetic interference (being electrically non-conductive, it cannot pick up nearby EM signals); very low attenuation loss (under 0.2 dB/km, so a single cable serves many kilometres); complete electrical insulation (no grounding or lightning-related issues); resistance to theft (it contains no valuable copper or similar metal); and better security of information (internal tapping or damage is very unlikely to go unnoticed).
PRISM BINOCULARS: ordinary binoculars using only two straight cylinders are limited in field of view, because the distance between the two barrels cannot exceed the distance between the two eyes. This limitation is overcome by placing two right-angled isosceles glass prisms (critical angle for glass , comfortably less than the internal angle of incidence inside such a prism, guaranteeing TIR) inside each barrel, which lets the wide-set objective lenses be optically 'folded' back to narrower, eye-spaced eyepieces -- improving both field of view and the perceived sense of depth.
PERISCOPE: used to view objects at or above a water's surface (or beyond an obstruction) from a position below/behind it, a periscope uses the very same isosceles right-angled-prism trick, TWICE in succession, each reflection turning the ray's path through a right angle -- once near the top opening, once again near the bottom, so the final image reaches the observer's eye travelling in the same original horizontal direction it started in. …
What this figure shows. Part (a), construction: a cutaway cross-section of a single optical fibre strand drawn as a set of concentric cylindrical layers -- a very thin central CORE (transparent, optically denser), surrounded by a CLADDING layer (transparent, optically rarer, smaller refractive index than the core), which is itself wrapped in an outer protective BUFFER layer and then a JACKET layer on the outside; each layer is labelled, showing the fibre's total thickness (under half a millimetre) is far less than a drawn human hair shown alongside for scale. Part (b), working: a longitudinal (lengthwise) section through just the core and cladding, showing a light ray entering one end of the core at a shallow angle and then bouncing back and forth in a zig-zag path along the length of the fibre, striking the core-cladding boundary repeatedly, each bounce drawn as a total internal reflection (angle of incidence at the boundary exceeding the core-cladding critical angle) that …
What this figure shows. A schematic of one barrel of a pair of prism binoculars: an objective lens on the far (object) side, an eyepiece lens on the near (eye) side, and, positioned in the light path between them, TWO right-angled isosceles glass prisms arranged so that light entering from the objective strikes the hypotenuse face of each prism from inside at an angle exceeding the glass-air critical angle (about 42 degrees, comfortably less than the prism's 45-degree internal incidence angle), undergoing total internal reflection at each prism in turn -- the two prisms are oriented so their combined effect folds/offsets the light path, letting the objective lenses of the two barrels be spaced farther apart than the two eyepieces (and the two eyes), widening the effect …
What this figure shows. A schematic of a simple periscope: a vertical tube open at both top and bottom, with a right-angled isosceles glass prism mounted at 45 degrees inside the tube at the TOP end and a second identical right-angled isosceles prism mounted at 45 degrees at the BOTTOM end. A horizontal ray of light entering the top opening strikes the hypotenuse of the top prism from inside, undergoes total internal reflection (angle of incidence about 45 degrees, exceeding the glass-air critical angle of about 42 degrees) and is turned through a right angle to travel straight DOWN the tube; on reaching the bottom prism it again strikes its hypotenuse face and undergoes a second total internal reflection, turning the ray through another right angle so it exits horizontally again at the bottom opening, towards the observer …
Worked out. A tiny LED sits at the centre of the bottom of a cylindrical vessel of diameter 6 cm and height 4 cm, filled completely with an optically dense liquid; the LED is visible from any inclined viewing position but only JUST visible when viewed exactly along the edge/rim of the vessel, meaning the ray reaching the rim leaves the liquid at grazing emergence, i.e. its angle of incidence inside the liquid at that point equals the critical angle ic. From the vessel's geometry (radius 3 cm, height 4 cm, giving a 3-4-5 right triangle from the LED to the rim, hypotenuse 5 cm), tan(ic)=3/4 identifies this as the 37-53-90 triangle, so sin(ic)=3/5, and the liquid's refractive index n …