Download the Mythical Man-Month Frederick P. Brooks, Jr., 1975

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Refraction of Light
form 3
陳達權 chan tat kuen
f.3d (5)
Physics Project
 Bending
 Apparent
 Inside
Light is not only what our eyes can see. In general
we call everything in the electromagnetic spectrum
– gamma rays and X-rays down to microwaves and
radio waves – light:
We can think of light as wave or particles – it has
wavelengths and frequencies and consists of
bending light
 Why
does the pencil / chopstick
appear bent?
bending light
Light ray is bent as it passes
from one medium to another.
It is due to light travelling at
different speeds in the two
It is called refraction of light.
As a result, the ray keeps the same
direction as before but is laterally
The ray is not bent only when it hits
the block at right angle.
density of medium
• Medium
– A transparent material through which
light travels
• When light passes
from a less dense
to a denser
medium, it is bent
towards the
density of medium
• When light passes
from a denser to a
less dense
medium, it is bent
away from the
• sin i is directly proportional to sin r
while i = angle of incidence &
r = angle of refraction
laws of refraction
When a ray of light passes from one medium to another,
 the incident ray, the refracted ray and the
normal all lie in the same plane,
 sin i is a constant
sin r
which is called Snell’s Law
Snell’s Law was discovered by Snell, a Dutch
scientist, in 1621 and so was named after him.
refractive index
The refractive index of a medium is
sin i
sin r
where i and r are the angle of incidence and
angle of refraction respectively when a ray of
light enters the medium from air.
Refractive indices of various materials
Refractive index
1.50 – 1.70
Example 1
A ray of light passes
from water into glass.
Given angle of
incidence is 30º.
1.33 sin 30º = 1.5 sin r
where r = angle of
r = 26.3º
Example 2
A light beam enters a
piece of glass from the
vacuum at 60º from the
normal as shown and
bends to 45º from the
normal once inside the
n sin(45º) = sin60º
where n = index of
refraction of
the glass
n = 1.22
Refraction by a Prism
A prism is a block of glass or
other transparent material,
usually having a triangular base.
When a beam of narrow white light
passes through a prism, the beam
is refracted and splits into all
the colours of the rainbow.
red orange yellow green blue indigo violet
The effect is called dispersion.
 有時暴雨後,天空中飄著許多小水滴;
Apparent Depth
 Why
does a swimming pool appear
shallower than it really is?
Real Depth vs Apparent Depth
Illustrated by the figure, the cone of rays from
O at the bottom of the swimming pool bend away
from the normal as it enters the air. When it
appears to come from I which is higher than O.
Real Depth vs Apparent Depth
 An
object placed under water or glass
appears to be higher than it actually is.
 the
depth that the object appears
= Apparent Depth
 The depth that the object is actually at
= Real Depth
Inside reflections
 the
inside surface of water as a
perfect mirror.
Total internal reflection
A ray of light hits the inside face of a
semicircular glass block.
The incident ray splits into two rays. The angle
of refraction is 90º and the refracted ray only
just manages to leave the glass surface.
Total internal reflection
When light travelling from a denser to a less
dense medium is incident on the interface at
an angle greater than the critical angle C
where C = sin-1 (1/n)
and n = refractive index of the material
Refractive index
Critical angle
1.50 – 1.70
36º - 42º
Fish-eye views
A fish or a diver under water can see everything
above the surface, but their view is squeezed
into a cone with an angle of 98º.
Fish-eye views
Outside this cone, the surface looks like a mirror
reflecting light from under the surface.
A photograph taken underwater looks like a
Prisms as perfect mirrors
A glass prism behaves like a perfect mirror if
light rays strike the inside face at an angle > 42º
(critical angle for glass). Prisms are used as
mirrors in periscopes and binoculars.
Example 3
The figure shows a pentaprism made of flint
glass of refractive index 1.58. Its upper face is
inclined at an angle of θ to the base.
critical angle C = sin-1 (1/1.58) = 39.3º
It is also the minimum angle of θ required for
light to be totally internally reflected by the
upper face.
Example 4
A diver carries a lamp below the surface of a
still lake (index of refraction of water is 1.33)
and circle of light is observed coming out of
the surface with a radius of 16 m. How far is
the diver below the surface?
critical angle C = sin-1 (1/1.33) = 48.8º
R/h = tan C
16m/h = tan 48.8º
h = 14.0 m
Refracting Telescopes
These are the first kind of telescopes
used, for example, by Galileo.
Refracting telescopes use lenses and the
principle of refraction, as shown above.
Reflections inside a diamond
The facets of a diamond have to be cut at
carefully chosen angles so that it can reflect
back light that goes into it.
refractive index of diamond = 2.42
critical angle for diamond-air interface
= sin-1(1/2.42) = 24.4º
Mirage 海市蜃樓
On a hot day in a desert, a driver may see
a pool of water at a distance.
What the driver sees is in fact a mirage. It
is just the reflection of the sky.
Layers of air near the
ground are hot. While
layers higher up are
cooler and denser,
and have higher
refractive indices.
Light from the sky is gradually refracted more
towards the horizontal.
It meets a layer of air near the ground at an
angle greater than the critical angle. Then total
internal reflection takes place. This reflection of
the sky looks like a pool of water to the driver.
 太陽的光可分解成赤、橙、黃、綠、藍
 空氣分子對波長較短的陽光,散射作用
Optical Fibre
Light can pass along thin glass fibre even the
fibre is bent. The ray of light bounces from one
side to the other and will not be lost to the air
from the sides.
An optical fibre cable is made up of a bundle of
thin glass fibre. It can be used for various
applications, such as data communication for
computers and TV programmes.
Optical Fibre
Advantages of using fibre cables
low transmission loss and wide bandwidth
small size and weight
immunity to interference
electrical isolation
signal security
abundant raw material
Useful links
[calculating unknown in Snell’s Law]
[refraction of light in different media]
[wave length, angle of incidence & medium]
[refraction of light simulation from one medium to another]