# 1.2.6 Total internal reflection by pharmphresh30

VIEWS: 11 PAGES: 9

• pg 1
```									1.2.6 Total internal reflection

Benson 35.4, p. 715

light ray starts in
optically denser medium

Snell's law:     n1 sin q1 = n2 sin q2 and n1 > n2,

so sin q2 > sin q1, so q2 > q1

angle of refraction is greater
than angle of incidence

q2
n2
e.g. air

n1 (> n2)                       water

"optically denser"     q1
medium
the angle of incidence can be increased to a
point when the angle of refraction becomes so
great that the refracted ray grazes along the
interface:
n                     q2 = 90∞
2

n1                    q1 = qc

"critical angle"
1

n1 sin qc = n2 sin 90∞      so        sin qc = n2 / n1

if the angle of incidence is increased any further,
no light gets refracted; instead all the light gets
reflected: total internal reflection
n2

n1
q1          q1
(> qc)
Example:
water surface

2 the entire world
around you appears
in this circle!

1 look up from under water

Note: in almost all cases of refraction some light
gets reflected (in the case of total internal reflection
all of it; total internal reflection reflects close
to 100% of the incident light, metal mirrors
refracted light
q2
n2

n1            q1      q1

some reflected light
1.2.7 Optical fibres & prism reflectors
Benson p. 716/717                   optically dense
10-50mm
material (e.g. glass)
incoming
light ray

total internal               light ray has been
reflections                 "guided" by fibre
extremely important to transmit information
because of much higher capacity than electrical wires
(lots of different colours at once!)

also used, for example,
in endoscopes:
"coherent fibre
each fibre transmits                      bundle"
one "pixel", the bundle
as a whole transmits
an entire image

pixels
Prism reflectors

Benson p. 716

prism reflector;
very high reflectivity!

reflected light ray

used, for example, in binoculars (to flip the image)
1.2.8 Dispersion & prisms

Benson 35.5, p. 717

the refractive index, n, is (slightly) different
for different colours

e.g. refractive index of glass
n

1.52

1.5

1.48

400             700     l [nm]

visible
range                 wavelength
violet                   red
functions of the wavelength, l
Snell's law:

n1 sin q1 = n2(l) sin q2(l)

different angles of diffraction

incident white
light ray

q1
n1

q2(red)
n2(l) q2(blue)
red
lig
blue

ht
ray
l
ight
ray

white light is "split" into
its colour components
diffractive "slab":

Benson p. 718

incident white
light ray
n1

n2(l)

n1
blu gre red
e en

displaced, but parallel
dispersion prism:

Benson p. 718                         angle of
n1     deviation
incident white
light ray
d

n2(l)                            red

bl
ue

rays with different colours
have different directions!

used in spectrometers (measure d, infer l)

```
To top