LightLightRefraction of LightRefraction of Light

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Learning Objectives

You will learn to•recall and use the terms used in refraction, including normal, angle of incidence and angle of refraction.•recall and apply the relationship sin i/sin r = constant to new situations or to solve related problems.•understand relative refractive index and absolute refractive index.•explain refraction by means of a change in speed of light in different optical media. •explain the terms critical angle and total internal reflection.•identify the main ideas in total internal reflection and apply them to the use of optical fibres in telecommunication and state the advantages of their use.

You will learn to•recall and use the terms used in refraction, including normal, angle of incidence and angle of refraction.•recall and apply the relationship sin i/sin r = constant to new situations or to solve related problems.•understand relative refractive index and absolute refractive index.•explain refraction by means of a change in speed of light in different optical media. •explain the terms critical angle and total internal reflection.•identify the main ideas in total internal reflection and apply them to the use of optical fibres in telecommunication and state the advantages of their use.

Definition:Definition:The change in direction, or bending of light when it passes from one medium to another medium of different optical density.

Do you notice something interesting about this picture?

RefractionRefraction

Incident ray is the light ray in 1st medium (air)

Refracted ray is the light ray in the 2nd medium (glass)

Normal is a line drawn perpendicular to the surface

Angle of incidence, i is the angle between the incident ray & the normal

Angle of refraction, r is the angle between the refracted ray & the normal

Optical density of a material is the ability of a material to allow light to pass through it

air (less dense)

glass (denser)

i

r

refraction of light

Example:

i will be greater than r

When a ray of light enters a denser medium, it bends TOWARDS the normal.

When a ray of light enters a less dense medium, it bends AWAY from the normal.

(a) From less dense TO denser medium:

glass (denser)

air (less dense)

incident ray

refracted ray

i

r

normaloriginal path of light ray

r will be greater than i

(b) From denser TO less dense medium:

original path

of light ray

glass (denser)

air (less dense)

incident ray

refracted ray

i

r

normal

refraction of light

refraction of light

r is greater than ir is lesser than i

Ray of light bends towards the normal when it enters a denser medium at an angle

Ray of light bends away from the normal when it enters a

less dense medium at an angle

During refraction, light bends first on passing from air to glass and again on passing from the glass to the air.

1. When light moves from air to glass (a denser material), it slows down and is refracted towards the normal.

2. When light moves from glass to air (a less dense material), it speeds up and is refracted away from the normal.

refraction of light

Try this….Complete the following diagrams to show the path of light rays through the glass blocks

air

glass

air

glass

air

glass

air

glass

air

(a) (b) (c)

(d)

refraction of light

Laws of Refraction

First Law: The incident ray, the normal and the refractedray all lie on the same plane.

Second Law: For 2 given media, the ratio sin i / sin r is aconstant, where i is the angle of incidence and r is theangle of refraction. (This is also known as Snell’s Law).

n1sinθ1 = n2sinθ2

Reflection vs Refraction

Reflection Refraction

Needs only 1 medium Needs 2 media

i = r sin i/sin r = constant

2 Laws of Reflection 2 Laws of Refraction

Refractive Index of MaterialsMedium Refractive Index (n)

Vacuum 1.00

Air 1.003

Water 1.33

Ethanol 1.36

Glycerine 1.47

Crown Glass 1.52

Quartz 1.54

Flint Glass 1.61

Diamond 2.42

Relative Refractive Index

The relative refractive index is the ratio of the absolute

refractive index of one material compared to that of

another, for example from water to glass.

Absolute Refractive Index

The absolute refractive index is the ratio compared with therefractive index of a vacuum.  (n for a vacuum = 1.00)

n1sinθ1 = n2sinθ2

ExampleA light ray strikes an air/water surface at an angle of 46° with respect tothe normal. The refractive index for water is 1.33. Find the angle ofrefraction when the direction of the ray is (a) from air to water and (b) from water to air.

(a) The incident ray is in the air, so θ1 = 46° and n1 = 1.00. The refracted ray is in water, so n2 = 1.33. Snell’s law can be used to find the angle of refraction θ2:

sinθ2 = (n1sinθ1)/n2 = (1.00 x sin46°)/1.33 = 0.54 θ2 = sin-10.54 = 33°

(b) With the incident ray in the water, we find that sinθ2 = (n1sinθ1)/n2 = (1.33 x sin46°)/1.00 = 0.96

θ2 = sin-10.96 = 74°

Therefore, for the case where the light ray is passing

from vacuum into a given medium, we could

simplify our equation to: n = sin i / sin r.

For the case where the light ray is passing from a

given medium to vacuum, we could simplify our

equation to: n = sin r / sin i.

Example

A ray of light is travelling from water (n = 1.33) toglass (n = 1.52) with an incident angle of 45.0°.Calculate the angle of refraction when the ray oflight enters the glass slab.

n1sinθ1 = n2sinθ2

1.33 x sin 45.0° = 1.52 x sin θ2

sin θ2 = (1.33 x sin 45.0°) / 1.52

θ2 = 38.2°

Refractive Index (n) of a Medium:

where i: angle of incidence (in less dense medium) r: angle of refraction (in denser medium) c: speed of light in vacuum (=3x108m/s) v: speed of light in medium

n = sin i / sin r = c / v

Example

If the speed of light in air is 3.0 x 108 ms-1, find thespeed of light in diamond (refractive index ofdiamond = 2.42)

n = c/v 2.42 = 3.0 x 108 / v v = 3.0 x 108 / 2.42

= 1.24 x 108 ms-1

To an observer standing at the side of a swimming pool,

objects under the water appear to be nearer the surface

than they really are. A similar effect can be seen when

"looking through" glass or any other transparent substance.

n = real depth / apparent depth.

An object seen in the water will usually appear to be at a different depth than it actually is, this is due to the refraction of light rays as they travel from the water into the air.

The first diagram shows that the observer ‘perceives’ that the chest appear to be closer to the surface than it really is.

Refraction - Effects of Refraction

Apparent depth

Effects of Refraction

In the diagram, refraction causes point A to appear nearer to the surface at B. So to the eyes, the straw appears to bend towards the surface of the water.

eye sees the virtual image of

the stick shallower than

it actually is

Total Internal Reflection

What happens when light passes from an optically denser medium to an optically less dense medium?

The critical angle is defined as the angle of incidence in the optically denser medium for which the angle of refraction in the optically less dense medium is 90°.

Total internal reflection is an optical phenomenon that occurs when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary, no light can pass through and all of the light is reflected.

For total internal reflection to occur, the following conditions

must be satisfied:

1) The light ray must travel from an optically denser medium towards an optically less dense medium.

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

Critical Angle & Refractive IndexConsider a light ray going from a denser medium to a less dense

medium (i.e. from glass to air). When angle of refraction is 90°, the

angle of incidence is known as the critical angle.

n = sin r / sin i = sin 90° / sin c

= 1 / sin c

sin c = 1 / n

Example

A right-angled prism (one of the angles of the prism is

90°) is made of glass of refractive index 1.5. A ray of light

enters the prism. Calculate the critical angle of the prism.

Using sin c = 1/n = 1/1.5 = 2/3

c = sin-1 (2/3)

= 41.8°

The Optical Fibres

An optical or fibre is a glass or plastic fiber that carries light along its length. Optical fibers are widely used in fiber-optic communications, which permits transmission over longer distances and at higher bandwidths (data rates) than other forms of communications. Fibers are used instead of metal wires because signals travel along them with less loss, they are also immune to electromagnetic interference and data security issues.

How optical fibre works

Light is kept in the core of the optical fiber by total internal reflection. This causes the fiber to act as a waveguide.

The core is optically more dense than the cladding. The light ray will undergo total internal reflection as it strikes the interface between the core and cladding as the incident ray has exceeded the critical angle.

References:

• http://www.photo.school.nz/lenses/bent_spoon.jpg• http://media.tiscali.co.uk/images/feeds/hutchinson/ency/dept0001.jpg• http://media-2.web.britannica.com/eb-media/73/1573-004-4FEB1C43.gif• http://www.optics4kids.com/terms/images/rightangleprism.gif • http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p028.shtm

l• http://commons.wikimedia.org/wiki/

File:Total_internal_reflection_of_Chelonia_mydas_.jpg• http://www.biocrawler.com/w/images/index.php?dir=e%2Fec%2F• http://www.fas.harvard.edu/~scidemos/LightOptics/FishTankTIR/

FishTankTIR.html• http://www.bd-associates.net/product/fiber.htm• http://laser.physics.sunysb.edu/~wise/wise187/2001/reports/andrea/report.html