Optical Biomedical Instrumentation - BMT 336

BMT Department
College of Applied Medical Sciences
King Saud University

Refraction
Lecture # 3

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Content:
• Refraction
➢Principle of Refraction
➢Index of Refraction (n)
➢Laws of Refraction
➢Dispersion
➢Fermat’s Principle for Refraction
➢Snell’s Law
➢Total Internal Reflection
➢Apparent Depth
➢Wavelength and Refraction
• Problems

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 Refraction

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 Behavior of Light Rays “waves” with MATTER (Review)
Light ray Light ray
Light ray
Refraction occurs when
light rays falls with an angle
Medium 1 on new medium and then
pass with an angle through
Medium 2
this medium.

• Transmission occurs when light rays falls • Reflection occurs when light rays hits an • This change in direction is dependent on the
vertically and through the object without object with very smooth surface and light’s wavelength and the index of
any change in the direction. bounces off. refraction (n) of the new medium.
• Example: Sun light falls with angle on water
• Example: Light coming through window. • Example: Light reflection from mirrors. or glass.

Light ray Light ray Light ray

Diffraction is the bending Absorption occurs when Scattering occurs when the
and spreading of waves photons from incident light incident light rays bounce off
around an obstacle. hit atoms and molecules and an object in many different
cause them to vibrate. directions.

• When light passes through a sufficiently-thin • Occurs when the incident light hits an • The amount of scattering depends on the
slit it will diffract and spread. object and causes its atoms to vibrate, size and structure of the object. Also it
converting the energy into heat. depends on the wavelength of the light.
• Example: Thomas Young double slit
experiment • Example: Sun and human skin • Example: Rayleigh scattering which gives
Cars with dark color the sky its blue color.
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 Reflection vs Refraction (Review)

• Figure shows some of the light incident

Normal
on a glass surface is reflected and some Incident Ray Reflected Ray
passed into the glass.

• The light that enters the glass is

partially absorbed and partially
transmitted.
Medium 1 ni θi θr
(Air) Interface
• The transmitted light usually undergoes
a change in direction, called refraction. Medium 2 nt
(Glass) θt

In the Reflection:
Incident angle (θi) = Reflected angle (θr)

In the Refraction:
ni Sin (θi) = nt Sin (θt)
Sin (θi) / Sin (θt) = nt /ni Refracted Ray
θi is the Incident angle, while θt is the refracted angle
n (Index of Refraction)
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 Principle Of Refraction

• As shown, light ray is entering from air into glass.

• The angle that incident beam makes with the normal to the surface is called incidence angle
(θi).
• The angle (θt) between the refracted beam and the normal is called the angle of refraction.
• In some books and websites, the symbol of the angle of refraction is (θr).
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 Principle Of Refraction
• Refraction explains familiar phenomena such as:
➢ Pencil appears to be bent at the surface of water.
➢ The fish appears closer to the surface than it really is.

Pencil in a glass of water Fish seams to be closer to the surface than actually is.

Apparent fish

Actual fish

The image adapted and modified from The image adapted and modified from https://slideplayer.com/slide/4527994/
https://etc.usf.edu/clippix/picture/refraction-of-pencil-in-cup-of-
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 Index of Refraction (n)
• The velocity of light in free-space c = 3x 108 m/s .
• The velocity of light in a material substance is generally less than the free space.
• The index of refraction “n” of a particular material is the ratio of the velocity of light (c) in
vacuum to the velocity of light through the material (v).

• It is a unit less quantity and is generally equal or greater than 1.

• The optical density of any transparent medium is a measure of its refractive index.
• A medium with a relatively high refractive index is said to have a high optical density, while
one with a low refractive index is said to have a low optical density.
• Optical density measures the amount of attenuation or intensity lost (by scattering) when
light passes through an optical component.
• The slower the light is able to travel through a given medium, the higher the optical density
of the medium.
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 Index of Refraction (n)
Index of refraction (n) in different medium:
Ethyl Crown Fused
Medium Air Water Ice Diamond
alcohol glass Quartz

n= 1 1.33 1.31 1.36 1.52 1.46 2.42

* Theses values apply for yellow light (λ= 589 nm).

Velocity of light in water vwater

Example: How long does it take for light to travel 250 m in water? (n = 1.33 for water).
Solution: The speed of light in water is = vwater = c/n ; n = 1.33, c = 3 x 108 m/s, d = 250 m.

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 The Laws of Refraction
• Two basic laws of refraction are:
1. The incident ray, the refracted ray and the normal to the interface of any two given
mediums, all lies in the same plane.
2. The path of a ray refracted at the interface between two media is exactly reversible.

(1) (2)

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 The Laws of Refraction
• Displacement of Light Passing Through the Glass:

The light incident on the glass first bent toward the normal as it passes through the denser
medium, and then it bent away from the normal as it returns to the air (less dense than glass).

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 Dispersion
• When polychromatic light (light containing more than one wavelength) passes through a refracting
prism, the prism will separate the light according to wavelengths, such separation is called chromatic
dispersion.
• Dispersion takes place because the refractive index of medium for different wavelengths (colors) is
different. For example, the bending of red component of white light is least, while bending is maximum
for violet.
1. With the light at the normal incidence, blue light (for which the index is higher, and the velocity is
less) will lag behind red light (red light travels faster).
2. With the light passing obliquely through a plane-parallel plate, the colors become separated, but the
rays remain parallel.
3. But with the prism, the rays spread apart.
• The angle subtended by the two colors is called the angular dispersion.
(1) (2) (3)

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 Dispersion

https://www.toppr.com/ask/content/concept/angular-dispersion-210298/

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 Dispersion
• Dispersion is also defined as (dn/dλ).
• The refractive index decreases as the wavelength increases.
• The rate of increase becomes greater at shorter wavelengths.

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 Fermat’s Principle for Refraction

• According to this principle, light takes the path of least

time.
• The time spent by light traveling from one point to another
is most often a minimum.
• Let S-S surface separate two media, and light goes from A to B. If the refractive index on either side
of the surface were the same, no matter what its magnitude, the path from A to B would be
straight line.
• If the two media have different indices, the path is no longer straight. Instead, the light is refracted.

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 Snell’s Law
The following relationships for light refraction in an
optical medium can easily be determined from Snell's
Sin (θ1) / Sin (θ2) = n2 /n1 law:
1. When light enters a denser medium, its speed decreases,
and the refracted ray is bent towards the normal.
2. When light enters a less dens medium, its speed
increases, and the refracted ray is bent away from the
normal.
3. There is no change in the direction of propagation, if there
is no change in index of refraction.

4. If a light ray goes from one

medium to another along the
normal, it is undeflected,
regardless of the change in
• Snell’s law tells us that when light passes from a less dense the index of the refraction.
medium to a high dense medium, then the light will be bent Although the angle does not
towards the surface normal. change, BUT the speed of
light does change as the light
• When light goes from high dense medium to a less dense travels from one medium to
medium, it is bent away from the surface normal. another.
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 Total Internal Reflection
• Total internal reflection can occur only when light is incident from a high dense medium (refractive
index n1) to a low dense medium (refractive index n2) (n1 > n2)
Consider the light source “S” is in the medium “1” and five rays A, B, C, D, and E are going in different
directions:
• Ray “A” passes into medium 2 normal to the interface:
(Incidence angle = refracted angle = 0)
• Ray “B” with incident angle “θ1” refracted away from the normal at an angle “θ2” (As n1 > n2, so θ2 > θ1).
• As the incidence angle “θ1” increases the refracted angle “θ2” also increases until at the critical angle “θc” the
refracted ray “D” emerges tangent to the surface.
• The critical angle “θc” is the limiting angle of incidence in a denser medium which results in an angle of refraction
of 90o.
• A Ray “E” with an angle greater than “θc” is reflected back
inside the medium “1” (total internal reflection), and Incidence
angle = reflection angle.

Critical angle “θc” can be calculated by using Snell’s law:

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 Total Internal Reflection
Since “sin θc” can never be greater than “1”, “n1” must be greater than “n2”. As the critical angle for glass
is 42o (arcsin (1/1.52) = 42o), so in many optical instruments 45o prisms are used.

In both cases total internal reflection occurs

because the angles of incidence are all 45o
(greater than critical angle)

• The diamonds are known for their impressive shining quality.

• Their shining quality is mainly due to the total internal reflection of light inside them.
• The critical angle for diamond-air interface is very small (About 24.4o).
• Once light enters a diamond total internal reflection takes place inside the diamond.
• The impressive shining quality of diamond is not by nature but because of the technical
skill of a diamond cutter.
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 Apparent Depth
Because of refraction, an object submerged in a liquid of higher of index of refraction
appear closer the surface than it actually is
Fish seams to be closer to the surface than actually is.

n1

n2
Apparent fish

Actual fish

The image adapted and modified from https://slideplayer.com/slide/4527994/

1 n1 (Where the human eye is located)

2
n2 (Where the object is located)
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 Wavelength and Refraction

• Light slows down when passing into a medium of

greater optical density.
• If c is the velocity of light in air, then it reduces to vm in
the medium.
• The frequency f remains the same in the medium.
• The wavelength of light is reduced when it enters a denser
medium

• As velocity decrease inside the medium, wavelength inside

the medium must decrease proportionality for the frequency
to remain constant. Dividing equation (1) by equation (2) Where nm is the index of refraction in the medium and λa is
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the wavelength of the light in air. 20
 Example 1:
A monochromatic ray of light in air enters a triangular prism whose absolute index of refraction is 1.50. The
prism is in the shape of isosceles right-angle triangle, and the incident ray is perpendicular to the surface as
shown. Complete the path of the light ray as it enters the prism.

Solution:

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 Example 2:
A beam of parallel light enters a block of ice at an angle of incidence 30o as shown. What is the angle of
refraction in the ice? (For ice n = 1.31)

Solution:

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 Problems
• P # 1. The speed of light through a certain medium is measured to 1.6 x 108 m/s. What is the index of refraction
for the medium? (Ans. 1.88)
• P # 2. Compute the speed of light in (a) crown glass (b) diamond (c) water and (d) ethyl alcohol.
(Ans. (a) 1.97 x 108 m/s (b) 1.24 x 108 m/s (c) 2.26 x 108 m/s (d) 2.21 x 108 m/s)
• P # 3. Light is incident at an angle of 37o from air to flint glass (n = 1.6). What is the angle of refraction into the
glass? What is the speed in the glass? (Ans. 22o, 1.88 x 108 m/s)
• P # 4. Light strikes from medium A into medium B at an angle of 35o with the horizontal boundary between the
two media. If the angle of refraction is also 35o, what is the relative index of refraction between the two media?
(Ans. 1.43)
• P # 5. A beam of light is incident on a plane surface separating two media of indexes 1.6 and 1.4. The angle of
incidence is 30o in the medium of higher index. What is the angle of refraction? (Ans. 34.8o)
• P # 6. What is the critical angle for (a) diamond (b) water and (d) ethyl alcohol if the exterior surface is air?
(Ans. (a) 24.4o (b) 48.8o (c) 47.3o)
• P # 7. The water in a swimming pool is 2 m deep. How deep does it appear to a person looking vertically down?
(Ans. 1.5 m)
• P # 8. The index of refraction of a certain glass is 1.5 for light whose wavelength is 600 nm in air. What is the
wavelength of the light as it passes through the glass? (Ans. 400 nm)
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