light continued

Light continued

Refraction of light is the bending of light as it goes from one optical medium to another

Less dense to more dense: bends towards normal

More dense to less dense: bends away from normal

A medium is

Index of RefractionMaterial Index of RefractionVacuum 1.0000

Air 1.0003Ice 1.3100

Water 1.3330Ethyl Alcohol 1.3600

Plexiglas 1.5100Crown Glass 1.5200

Light Flint Glass 1.5800Dense Flint Glass 1.6600

Zircon 1.9230Diamond 2.4170

Rutile 2.9070Gallium phosphide 3.5000

Incident ray

Refracted ray

Glass block

i

r

The Laws of Refraction of Light

1. The incident ray, the normal and the refracted ray all lie in the same plane

2. where n is a constant

This is called Snell’s Law

nrsin isin

When light travels from a rarer to a denser medium it is refracted towards the normal e.g. air to water

when light travels from a denser to a rarer medium it is refracted away from the normal e.g. glass to air

Experiment to Verify Snell’s Law and determine the refractive index of glass

12

34

Block of glass

i

r

Experiment to Verify Snell’s Law and determine the refractive index of glass

Method1. Outline the glass block on paper2. Stick pins 1 and 2 in the paper in front

of the block3. Stick pins 3 and 4 in line with the

images of 1 and 2, as seen through the block

4. Remove the pins, join the pinholes and draw the normal

5. Measure angles i and r6. Repeat for different angles of incidence7. Draw a graph of sin i vs. sin r8. The slope of the graph is the refractive

index of glass

Result

i r Sin i Sin r Sin i/Sin r

Sin i

Sin r

Slope of graph =

Thus the refractive index of glass is ____

12

22

xxyy

ConclusionThe graph is a straight line graph

through the origin, thus verifying Snell’s Law

The slope of the graph gave the refractive index of glass

Real and Apparent Depth

A swimming pool appears to be less deep than it actually is, due to refraction at the surface of the water

We can calculate the refractive index of a liquid by using

n = depthApparent depth Real

Refractive index

n =

rsin isin

depthApparent depth Real

CSin 1

mediumin light of speedairin light of speed

Question 1

When light passes from air into a liquid, the angle of incidence and refraction are 57˚and 30˚ respectively. Calculate the refractive index of the liquid.

Answer Formula:

nSinrSini

68.13057

SinSin

Question 2

A ray of light is incident at 35˚ on (a) a glass surface and (b) a water surface. Calculate the angle of refraction given that,

ng=1.52 nw=1.33 Answer

Formula: nSiniSinrn

SinrSini

Textbook Examples

Questions 1-3 on page 31

Total Internal Reflection

This may occur when light goes from a denser to a less dense medium

As i is increased so is rEventually r = 90˚At this point i has reached the ‘critical

angle’

r = 90˚

i = critical angle

Total Internal Reflection!!!

If i is increased beyond the critical angle, the ray does not enter the second medium

It is reflected back into the first mediumWe can also find the refractive index of a

material using

n = CSin 1

C = critical angle

Example

The critical angle of glass is 41.81˚Find the refractive index of glassn =

n = 1/0.666

n = 1.5

CSin 1

Refractive index

n =

rsin isin

depthApparent depth Real

CSin 1

mediumin light of speedairin light of speed

ExampleThe refractive index of glass is 1.5This value is for a ray of light

travelling from air into glass

So ang = 1.5 =

Or gna = =

Asin Bsin

5.11

Bsin Asin

Applications of Total Internal Reflection

Periscopes (using a prism)Diamonds and bicycle reflectorsOptical fibres – in telecommunications

and by doctors

Prisms

Prisms are considered to be better than mirrors for reflecting light. This is because they use total internal reflection.

This is the reason prisms are used in periscopes and binoculars.

Optical Fibres

Total Internal Reflection has given rise to the use of optical fibres.

The signal is fired at an angle greater than the critical angle so that it is reflected all the way along the fibre.

The light is therefore trapped within the fibre. This technology is used to transmit information over long distances.

Endoscopes

These are used in medicine. They contain two bundles of optical fibres, one to carry light to the organ being viewed and the other to carry the image of the organ back to the operator.

44

Optic Fibre

Glass core of high refractive index

Glass cladding of low refractive index

45

Normal

NN N

Glass of high refractive index

Glass of low refractive index

Remember that rays are path-reversible

AIR

GLASS

A

B

Mirages

Mirages are caused by the refraction of light in air due to temperature variations

SKY

LENSES

Made of transparent material, usually glass

Convex lens (converging)

Thick in centre and thin at edges

Concave lens (diverging)

Thin in the centre and thick at the edges

Ray diagrams for lenses

1. Ray incident parallel to principal axis is reflected out through focus

2. Ray incident through focus is reflected out parallel to axis

3. Ray incident through optic centre continues in straight line

f2f f

RAY DIAGRAMS FOR CONVEX LENSES

Optic centre

f2f f

RAY DIAGRAMS FOR CONCAVE LENSES

Optic centre

Geometric Optics 2.03

The image in a concave lens is always virtual, erect, and diminished

Concave lens always has negative f and v

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Lens formulae

m =

m =

uv

object ofheight image ofheight

vuf111

Example

An object is placed 10cm away from a convex lens of focal length 12 cm. Calculate the nature, position and magnification of the image.

f = 12u = 10v = ?

v = -60cm

vuf111

v1

101

121

v1

101

121

v1

601

m =

m = = 6

So the image is formed 60cm from the lensIt is virtualMagnification is 6

uv

1060

Example 2

An object is placed 40cm from a concave lens of focal length 50cm. Find the position, nature and magnification of the image.

u = 40cmf = -50cmv = ??

v = -22.2 cm

vuf111

v1

401

501

v1

401

501

v1

2009

m =

m = = 0.56

So the image is formed 22.2cm from the lensIt is virtualMagnification is 0.56

uv

402.22

Experiment to Measure the Focal Length of a Convex Lens

F

Plane mirror

Pin

Convex lens

Experiment to Measure the Focal Length of a Convex Lens

Method A rough estimate of the focal length may first

be obtained by focusing the image of a distant object on a sheet of paper

1. Set up the apparatus as in the diagram2. Move the pin in and out until there is no

parallax between the pin and its image3. Measure the distance from the pin to the

centre of the lens. This is the focal length

ResultThe distance from the pin to the centre of

the lens was ______

ConclusionThe focal length of the lens is ______

Experiment to Measure the Focal Length of a Concave Lens

F

Plane mirror

Pin

Convex lens

Concave lens

Method1. Set up the apparatus as in the diagram2. The focal length of the convex lens is first

measured3. The concave lens is combined with the convex

lens (of shorter focal length), and so overall it behaves as a convex lens

4. Move the pin in and out until there is no parallax between the pin and its image

5. Measure the distance from the pin to the centre of the lens. This is the focal length of the combination

Results

The focal length of the convex lens is 22cm The focal length of the combination is 51cm. The focal length of the concave lens can be

calculated from the formula

Where F = focal length of combinationf1 = focal length of convex lensf2 = focal length of concave lens

21

111ffF

F = 51cmf1 = 22

f2 = ??

21

111ffF

f1

221

511

f1

221

511

f1

11225122

f1

112229

cmf 69.38

Conclusion

The focal length of the concave lens is 38.69cm