Chapter three
Light
Light is a form of energy.
The sun is the main source of energy on earth surface.
The energy from the sun is almost divided between heat and light.
The plants need light to carry out photosynthesis process to make food.
Light has a wave nature as it can reflect, refract, interfere and diffract.
Light is an electromagnetic wave which doesn't need medium to
transmit through, it consists of vibrating electric and magnetic fields,
oscillate at equal frequency at the same phase normal to each other and
normal to the direction of propagation.
Light is a transverse wave consisting of crests and trough.
They travel at constant speed in space (3x𝟏𝟎𝟖 m/s).
The electromagnetic spectrum
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When the light ray falls on a separating surface between two optical
media which are different in optical densities, part of it will reflect and
the other part will refract neglecting the absorbed part by medium.
Reflection of light
Reflection of light: it's the rebounding (return back) of the light rays in
the same medium when they meet a reflecting surface.
Laws of reflection
The angle of incidence = the angle of
reflection.
The incident ray, the reflected ray and
the normal to the reflecting surface at
the point of incidence all lie in one
plane to the reflecting surface.
When a light ray falls normally to the
reflecting surface, it reflects on itself.
Because the angle of incidence = the
angle of reflection = 0.
Refraction of light
Reflection of light: it's the bending (changing in the path) of the light
rays when they pass from a medium to another one having different
optical density.
Occurrence of light refraction isDue to the difference in the speed of
light in the two media.
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Optical density: the ability of the medium to bend light rays.
The ratio between the sine of the
angle of incidence in the 1st medium
to the sine of angle of refraction in
the 2nd medium is equal to the ratio
between the speed of light in the two
media.
𝑉1 sin 𝛷 𝜆1
𝑛2
=
=
= 1𝑛2 =
𝑉2 sin 𝜃 𝜆2
𝑛1
The incident ray, the refracted ray
and the normal to the separating
surface (interface) at the point of
incidence all lie in one plane to the
separating surface.
Relative refractive index:It's the ratio between the speed of light in the
1st medium to the speed of light in the 2nd medium.
It's the ratio between the absolute refraction index of the second
medium to the absolute refraction index of the first one.
It's the ratio between the sin the angle of incidence in the first medium
to sin the angle of refraction in the second medium.
Absolute refractive index for a medium: It's the ratio between the
speed of light in space (or air) to the speed of light in this medium.
Note:
The speed of light in space (c) is one of the physical constants in the
universe. (c = 3 x 108 m/s).
The speed of light in space is greater than the speed of light in other
media.
𝑐
𝑐
𝑐
𝑐 𝑉1 sin 𝛷
𝑛1 =
, 𝑆𝑜 𝑉1 =
& 𝑛2 =
, 𝑆𝑜 𝑉2 =
&
=
=
𝑉1
𝑛1
𝑉2
𝑛1 𝑉2 sin 𝜃
𝑐
𝑛1
𝑐
𝑛2
sin 𝛷 𝑛2
=
= 1𝑛2, 𝑆𝑜 𝑛1 ∗ 𝑠𝑖𝑛𝛷 = 𝑛2 ∗ 𝑠𝑖𝑛𝜃 𝑆𝑛𝑒𝑙𝑙 ′ 𝑠 𝐿𝑎𝑤
sin 𝜃 𝑛1
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Snell's Law: the product of the absolute refractive index of the first and
sine the angle of incidence in it equal the product of the absolute
refractive index of the second medium and sine the refraction angle in it.
We can use refraction to analyze a white light ray into its components of
different wavelengths (light spectrum-ROYGBIV) as the absolute
refractive index of the medium differs according to the wavelength of
each color.
When a light ray passes from a medium to
denser medium, it bends towards the normal
(𝛷 > 𝜃, 𝑉1 > 𝑉2, 𝑛1 < 𝑛2, 1𝑛2 > 1)
When a light ray passes from a medium to
less denser medium, it bends away from the
normal (𝛷 > 𝜃, 𝑉1 > 𝑉2, 𝑛1 < 𝑛2, 1𝑛2 > 1)
When a light ray falls normal on the
separating surface, it doesn't refract
Interference of light
Interference of light: it’s superposition of two light waves having same
frequency and in phase (same velocity & direction) so the intensity of
the light reinforced at some positions (illuminated-bright- fringes) and
it’s weakened in other position (dark fringes).
Double Slit experiment (Thomas Young):
Monochromatic light: it’s light source with constant wavelength (red
light recommended). Like sodium lamp.
Coherent sources: they are light sources that emit waves of same
frequency, amplitude and in phase (same direction & velocity).
Young’s double slits experiment:
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Usage:
Used to explain the interference of light waves and calculate the wave
length of any monochromatic light.
Steps:
 A source of monochromatic light is placed at a suitable distance
from a screen having two narrow slits.
 Cylindrical waves (from the two slits acting as two coherent
sources) interfere with each other.
 The result interference is received on another screen in form of
bright and dark fringes.
 We can calculate the wavelength of the monochromatic light from
the following equation:
𝛥𝑦 =
λ∗R
Δy ∗ d
𝑠𝑜 λ =
𝑑
R
Where:
λ: is the wavelength of the monochromatic light.
R: is the distance between the two double slits screen and the receiving
one.
d: is the distance between the two slits.
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Notes:
If the different path = m*λ where m is (0, 1, 2,…) bright fringe appears.
If the different path = (m+0.5)*λ where m is (0, 1, 2,…) dark fringe
appears.
The central fringe is always bright due to the path difference is zero so
the constructive interference occurs (two crests or two troughs
meeting). The intensity of light increase forming bright fringe.
The condition to obtain clear interference fringes:
 Present of two coherent light sources.
 The coherent sources must be close to each other (decrease d).
 Used monochromatic light source with high wavelength (increase
λ).
 The size of any of the slits must be smaller than the wavelength of
the incident waves. (Diffraction).
Diffraction of light
Diffraction
Airy Disk
Diffraction of light: it’s the formation of a circular spot with bright and
dark fringes (called Airy disk) due to flaring out monochromatic light as it
passes through a small hole or solid edge (instead of passing in straight
line).
Critical Angle and Total internal reflection
Critical angle (Фc): it’s the angle of incidence in the denser medium
when the angle of refraction in the less one is 90 ˚.
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From the Snell’s law
n1*sinФ = n2*sinθ As θ = 90˚ For Фc so sin90 = 1.
n1*sinФc = n2 so sinФc =
𝑛2
𝑛1
=1n2.
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For air sinФc = .
𝑛1
Notes:
n1 is always greater than n2.
Increasing the difference between n1 and n2 decreasing the critical
angle.
The absolute refractive index of a medium = the reciprocal of the sin of
critical angle.
The value of the critical angle is inversely proportional to the absolute
refractive index of the medium.
Application of total internal reflection
Optical fibers:
Optical fiber: it’s a thin flexible tube made of a transparent material (like
glass fibers) used to transmitting light energy based on total internal
reflection as following:
In medical (Endoscopes): transmitting images of internal parts of body.
In communication: using laser to transmit the electric signals.
How it works: Light rays enter the optical fiber with angle of incidence
greater than the critical angle so they suffer total internal reflection till it
emerges from the other end.
Totally reflecting prisms:
Triangle glass prism of (90ᵒ-45ᵒ-45ᵒ) used in:
Changing the path of light rays by 90ᵒ or 180ᵒ (angle of emergence).
Periscopes and Binocular.
Changing the upper and lower light rays of an image with each other.
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Notes:
Totally reflecting prisms is better than plane mirrors in reflecting
metallic surface because they reflect 100% of incident light rays and
don’t lose their luster but mirrors do.
The face of reflecting prism covered with a thin layer of Cryolite
(Aluminum fluoride) or magnesium fluoride because they have a less
refractive index than glass to minimize the loss of light intensity.
Mirage:
Mirage: it’s a natural phenomenon occurs in hot regions at noon in hot
day where false images appear.
Examples: See false images above water surface, see water image on the
paved road.
Explanation: the light rays pass from cold air layers to hotter one so
refract away from the normal till the angle of incidence is greater than
the critical angle so total reflection occurs producing false image.
Deviation in triangular prism
Angle of deviation (α): it’s the angle between the extension of the
incidence ray and the emergent ray.
Prim rules Prove:
Ф1: the angle of incidence (from air to glass).
Ѳ1: the angle of refraction.
Ф2: the internal angle of incidence (2nd).
Ѳ1: angle of deviation.
A: the prism angle, Apex, vertex angle or reflective angle.
The rule of prism angle
A + E = 180ᵒ (OBEC cyclic quadrilateral).
Ѳ1 + Ф2 + E = 180ᵒ (BCE triangle).
A = Ѳ1 + Ф2
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The rules of angle of deviation:
α = 1 + 2 (exterior angle).
Ф1 = 1 + Ѳ1. So 1 = Ф1-Ѳ1
Ѳ2 = 2 + Ф2. So 1 = Ѳ2-Ф2
α = (Ф1-Ѳ1) + (Ѳ2-Ф2) = (Ф1+ Ѳ2) - (Ѳ1+ Ф2)
α = (Ф1+ Ѳ2) – A
The angle of deviation (α) & the angle of incidence (Ф) relation.
From experiment: Increasing angle of incidence decreasing angle of
deviation till a certain value (Minimum deviation) then increase again.
Minimum deviation position view:
The angle of incidence (Ф1) = the angle of emergency (Ѳ2).
The internal angle of incidence (Ф2) = the angle of refraction (Ѳ1).
The white light separated into its seven colors.
𝑛=
sin Ф1
sin Ѳ1
=
sin Ѳ2
sin Ф2
Rules of prism angle at min deviation:
A = Ф2+Ѳ1 = 2Ѳ1 so Ѳ1 =
𝐴
2
αᵒ = Ф1+Ѳ2-A = 2Ф1-2Ѳ1, so Ф1 =
𝛼ᵒ+2Ѳ
2
=
𝛼ᵒ+𝐴
2
𝜶ᵒ+𝑨
𝐬𝐢𝐧(
)
sin Ф1
𝟐
𝑛=
, 𝑆𝑜 𝒏 =
𝑨
sin Ѳ1
𝐬𝐢𝐧( )
𝟐
Where:
n: the refractive of index of prism.
αᵒ: the angle of min deviation.
A: the prism angle.
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