Refraction of Light

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Refraction is the change in direction of light when it passes from one medium to another.

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If light ray enters another medium perpendicular to boundary, the ray does not bend.

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When the light ray travels from air to water, the refracted ray bends towards the normal.

i

r

air

water

Incident ray

Refracted ray

normal

i – angle of incidence

r– angle of refraction

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When the light ray travels from water to air, the refracted ray bends away from the normal.

i

rair

water

Incident ray

Refracted ray

normal

i – angle of incidence

r– angle of refraction

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During refraction, light bends first on passing

from air to glass and again on passing from

the glass to the air.

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During refraction, light bends first on passing

from air to glass and again on passing from

the glass to the air.

i

r

Incident ray

Emergent ray

Refracted ray

Reflected rayair

air

glass

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Light slows down when it enters an optically denser medium. The refracted ray bends towards the normal when the second medium is optically more dense than the first.

i

r

air

water

Incident ray

Refracted ray

normal

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Light speeds up when it enters an optically less dense medium. The refracted ray bends away from the normal when the second medium is optically less dense than the first.

air

water i

r

Incident ray

Refracted ray

normal

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Among the 3 transparent mediums (air, water and glass), glass has the highest optical density.

air

water

i 1

r 1

Incident ray

Refracted ray

glass

i 2

r 2

Refracted ray

air

water

i 1

r 1

Incident ray

glass

i 2

r 2

Refracted ray

Refracted ray

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Complete these ray diagrams.

air

glass glass

water

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Complete these ray diagrams.

airwater

glassair

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The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.

For two given media, the ratio sin i ÷ sin r is a constant,

where i is the angle of incidence and r is the angle

of refraction

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i

r

air

water

Incident ray

Refracted ray

normal

Refractive Index, n =

sin i

sin r

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The higher the optical density, the greater the refractive index. The greater the refractive index, the

greater the bending of light towards the normal.

air

water

i 1

r 1

Incident ray

Refracted ray

glass

i 2

r 2

Refracted ray

air

water

i 1

r 1

Incident ray

glass

i 2

r 2

Refracted ray

Refracted ray

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If light is incident upon a piece of glass (refractive index 1.52) at an angle of 45o, what is the angle of

refraction?

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Given that the refractive index of water is 1.33, calculate the angle of refraction when the incident

ray comes in at 60o to the normal.

60 o

r

air

water

Solutionn = sin i

sin r

1.33 = sin 60 o

sin r

s in r =

sin 60 o

1.33

r = 40.6 o

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When light travels from a less dense medium to a

denser medium…

n = sin isin r

i

r

a ir

water

When light travels from a denser medium to a less

dense medium…

n = sin rs in i

i

rair

water

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The figure shows light travelling from water into the air. The ray is incident upon the boundary at 30o. What is the angle of

refraction if the refractive index of water is 1.33?

30 o

rair

water

Solution

n sin rsin i=

1.33 sin 30 o

sin r=

sin r= 1.33sin 30 o

r =

41.9 o

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Other ways of calculating the refractive index…

Refractive index, n =

Speed of light in vacuum / air

Speed of light in medium

=

c

v

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Take a look at this...

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The critical angle is the angle of incidence in the optically denser medium for which the angle of refraction is 90o.

When i = critical angle,c r = 90o.

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This is called TOTAL INTERNAL REFLECTION.

When i > critical angle, the ray gets reflected internally.

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For TOTAL INTERNAL REFLECTION to take place:

The light ray must travel from an optically denser medium towards a less dense one.

The angle of incidence must be greater than the critical angle.

Direction of light path

i

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How do we calculate the critical angle?

We know that r = 90o…

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We know that when light travels from a less

dense medium to a denser medium

Refractive Index, n =

sin r

sin i

We know that when light travels from a denser medium to a less dense medium

Refractive Index, n =

sin r

sin i

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How do we calculate the critical angle?

We know that r = 90o…

Refractive Index, n =

sin rsin i

n =sin csin 90o

=sin c

1

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How do we calculate the critical angle?

n=sin c

=c

1

sin-1

n

1

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Medium:

Refractive Index:

Critical Angle:=c sin-1

n

1

Glass

1.50

= sin-1

1.50

1

= 41.8o

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Medium:

Refractive Index:

Critical Angle:=c sin-1

n

1

Water

1.33

= sin-1

1.33

1

= 48.8o

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Medium:

Refractive Index:

Critical Angle:=c sin-1

n

1

Diamond

2.42

= sin-1

2.42

1

= 24.4o

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Total Internal Reflection in Prisms

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Total Internal Reflection in Prisms

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Fibre Optics