Lesson 16

Dispersion

General Physics 2
1/2
Science, Technology, Engineering, and Mathematics
“There’s a rainbow after the rain.” STEM

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 STEM

This saying will not

only make you
optimistic once in
while, but did you
know that this is also
scientifically accurate?
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 STEM

What exactly are colors? Where

do they come from?

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 Learning Objectives
At the end of the lesson, you should be able to do the following: STEM

● Explain the concept of light dispersion.

● Apply Snell’s law to explain the dispersive property

of light.

● Determine the applications of dispersion in daily

life.

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 Rainbows STEM

● Light rays from the sun

refract as they pass through
the air to water droplets in
the atmosphere, as shown.
● This is the reason why there
is always a rainbow after a
rain.

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 RAINBOW PROCESS STEM

● Dispersion of Light: Sunlight appears white to us, but it's actually made up of a spectrum of colors, each with a
different wavelength. This is called dispersion. When sunlight passes through a prism, it breaks into its component
colors.

● Reflection and Refraction: When sunlight encounters raindrops suspended in the air, some of the light is reflected
off the surface of the droplet, while some enters the droplet and is refracted (bent) as it passes from air into water.

● Internal Reflection: Once inside the droplet, the light undergoes multiple internal reflections off the inner surface of
the droplet. This causes the light to spread out and be dispersed further.

● Exit and Refraction: Eventually, the light exits the droplet. As it exits, it is refracted again, bending once more as it
moves from water back into air.

● Rainbow Formation: The dispersed light exits the droplet at different angles depending on its color. Each color of
light is refracted at a slightly different angle, spreading out the colors and creating the familiar spectrum of a
rainbow.

● Observation Angle: To see a rainbow, you need to be in the right position relative to the sun and the rain. Rainbows
are always opposite the sun in the sky, so you'll need to have the sun behind you and rain or mist in front of you to
see a rainbow.

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STEM

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 The Prismatic Effect STEM

● An optical prism is defined as a refractive

transparent material with precise angles and plane
faces.

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 The Prismatic Effect STEM

● The formation of
rainbows by dispersion is
explained by the same
physics responsible for
the multi-color splitting
of light when it passes
through a prism.
● This is called the
prismatic effect.
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 Dispersion STEM

● Dispersion refers to the

scattering of white visible
light into a full spectrum
of wavelengths as shown
by the prismatic effect in
the diagram.
● From white light, it was
dispersed into different
colors.
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 Dispersion STEM

● Colors are, in fact, different wavelengths of visible

light travelling at different speeds across different
media, as shown.

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 Dispersion STEM

The Effect of the Refractive Index in Light Dispersion

● You know from Snell’s law that the refractive index

(constant for a particular medium) affects the angle
of refraction of a light ray. For a given medium, this
refractive index n is, in turn, affected by the
wavelength of light.
● The refractive index and the wavelength are
inversely proportional.
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 Dispersion STEM

Refractive index of some media at different wavelengths.

Red Orange Yellow Green Blue Violet

Medium
660 nm 610 nm 580 nm 550 nm 470 nm 410 nm

water 1.331 1.332 1.333 1.335 1.338 1.342

diamond 2.410 2.415 2.417 2.426 2.444 2.458

crown
1.512 1.514 1.518 1.519 1.524 1.530
glass
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 STEM

How does the refractive index of

a material affect the
wavelength of a particular
color?

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Remember STEM

The refractive index and the wavelength

are inversely proportional. Thus, n
decreases as the wavelength lengthens
and the opposite holds true. This
explains why violet, which has the
shortest wavelength, bends more in a
prism as other colors do.

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 The Angle of Deviation STEM

● The net refraction caused by the prismatic effect

can be described by the angle of deviation.
● It refers to the angle formed between:
(1) the light’s incident ray entering the face of the
prism adjacent to the light source (we will call this
the first face); and
(2) the refracted ray that comes out of the prism’s
second face.

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 The Angle of Deviation STEM

The angle of deviation relative to the angles of incidence and emergence

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 The Angle of Deviation STEM

● Since refractive indices vary across different visible

light wavelengths, the angle of deviation 𝛿
(lowercase Greek letter delta) also differs
correspondingly.

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 The Angle of Deviation STEM

● Colors with shorter wavelengths (blue and violet)

deviate more from their initial path than do those
with longer wavelengths (red, orange, and yellow),
as shown.

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 Dispersion STEM

● Since dispersion is an application of Snell’s law, the

same equation will be used to solve for the values
of the refractive indices, the angle of incidence, and
the angle of refraction.
● Recall that these variables are related by the law of
refraction in:

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Dispersion STEM

Minimum deviation in a triangular prism

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 STEM

How does the angle of incidence

affect the angle of deviation in a
regular prism?

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 Let’s Practice! STEM

A light ray passing through the first face of a prism is

measured at 1.58 × 108 m/s. What is the prism’s
refractive index?

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 Let’s Practice! STEM

A light ray passing through the first face of a prism is

measured at 1.58 × 108 m/s. What is the prism’s
refractive index?

The refractive index of the unknown material is 1.90.

This is the refractive index of a solid garnet stone.
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Try It! STEM

The speed of a light ray through a prism

has been measured at 2.74 × 108 m/s.
Determine the prism’s refractive index.

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 Let’s Practice! STEM

A red light ray with a wavelength of 700 nm hits

incident on the first face of a fused quartz prism and
formed an angle with respect to the normal of 69.59°
(shown below). If its refractive index n700nm is 1.46
and the initial environment is air, what is the angle
of refraction at the first face of the prism?

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 Let’s Practice! STEM

A red light ray with a wavelength of 700

nm hits incident on the first face of a
fused quartz prism and formed an angle
with respect to the normal of 69.59°
(shown below). If its refractive index n700nm
is 1.46 and the initial environment is air,
what is the angle of refraction at the first
face of the prism?

The angle of refraction is 39.95°.

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Try It! STEM

Suppose that the triangular prism below is

made of diamond instead, and the prism is
submerged underwater. Determine the
angle of refraction at the water-first face
interface if the angle of incidence is 16°
with respect to the normal to the surface.

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 Let’s Practice! STEM

Standing on top of a lone hill

at dusk, a trekker observes
a rainbow, as shown at the
right. Suppose that it is 8.0
km away and the valley is
2.0 km below the flat-topped
hill’s peak. What fraction of
the rainbow’s arc can the
trekker see?
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 Let’s Practice! STEM

Standing on top of a lone hill at

dusk, a trekker observes a
rainbow, as shown at the right.
Suppose that it is 8.0 km away and
the valley is 2.0 km below the flat-
topped hill’s peak. What fraction
of the rainbow’s arc can the
trekker see?

The visible fraction of the rainbow with respect to the

trekker is 62.22% of the entire arc.
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Try It! STEM

If the rainbow’s location is on a valley

10.12 km away from the trekker and
1.45 km below the flat hill’s peak,
determine the fraction of the rainbow’s
arc visible to the trekker if the rainbow
is found 40°and 42° from the hiker’s
shadow.

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 Check Your Understanding STEM

Identify what is being referred to in each of the

following statements.
1. Total internal reflection refers to the scattering of white
visible light into a full spectrum of wavelengths.
2. The refractive index and the wavelength are inversely
proportional.
3. An optical prism is defined as an opaque material with
precise angles and plane faces.

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 Check Your Understanding STEM

Calculate the angle of refraction at each interface (1

point) and trace the path of the light ray through each
medium’s surface (1 point). Consider the angle of
incidence at the first interface to be 30° and use a
protractor to accurately trace the light ray’s paths.

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 Let’s Sum It Up! STEM

● The formation of rainbows by dispersion is

explained by the same physics responsible for the
multi-color splitting of light when it passes
through a prism. This is called dispersion, or the
prismatic effect.
● Dispersion refers to the scattering of white
visible light into a full spectrum of wavelengths.

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 Let’s Sum It Up! STEM

● The refractive index and the wavelength are

inversely proportional. Thus, n decreases as the
wavelength increases and the opposite holds true.
● The angle of deviation refers to the angle formed
between (1) the light’s incident ray entering the
face of the prism adjacent to the light source (we
will call this the first face) and (2) the refracted ray
that comes out of the prism’s second face.
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 Let’s Sum It Up! STEM

● As the angle of incidence θa increases, the angle of

deviation initially decreases until it reaches its
minimum (this is also called minimum deviation or
𝛿min) and increases once again.
● Minimum deviation occurs when the light’s path
within the prism is parallel to the base.

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 Key Formula STEM

Concept Formula Description

Use this
Dispersion in
where relationship to
Prisms (as
● na is the refractive index of the derive the
explained by
material with incident ray; formulas for the
Snell’s Law)
● θa is the angle of incidence from unknown
the normal to the surface; values of either
● nb is the refractive index of the the na, θa, nb,
material with refracted ray; and
and the θb when
● θb is the angle of refraction from
light disperses in
the normal to the surface
a prism.
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Challenge Yourself STEM

Explain the phenomenon of

dispersion using Snell’s Law.

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