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11 Reflection and Refraction

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Introduction

To explain how light behaves, we can think of light travelling as rays.A ray travels in a straight line. It will change direction if:• It is reflected (when it strikes a surface)• It is refracted (when it passes from one material

to another).We can also think of light as wavesLaws of reflectionThe laws of reflection tells us where a ray will go when it is reflected.The normal is the line at 90o to the reflecting surface at the point where the incident ray strikes it

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normalincident ray reflected rayi r

Law 1: angle of incidence = angle of reflection, i = r (angles measured from the normal to the ray)

Law 2: incident ray, reflected ray and the normal are all in the same plane.

These laws not only apply for flat surfaces but also for curved and rough surfaces

normal

i r ir

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Refraction: when it happensLight travels fastest in a vacuum. It travels more slowly in other media.When light changes speed (because it travels from one medium to another), it is refracted.• If a ray enters a medium head-on (angle of

incidence i = 0), it travels straight on.• If a ray enters a medium obliquely, it bends

Laws of refractionAs with reflection, angles are measured from the normal to the ray.Law 1: Snell’s law explains how the angles of incidence and refraction are related.Law 2: incident ray, refracted ray and the normal are all in the same plane.

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normalr r

i i

Note that r is now the angle of refraction, not reflectionRefractive index nThe refractive index, n of a medium relates the speed of light in the medium to the speed of light in free space (vacuum)

Refractive index, n =

speed of light in free space speed of light in medium

n =

c0

cmedium

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Refractive index nIn a medium of refractive index 2, light travels at half its speed in free space (vacuum). Some values of n are worth remembering:n0 = 1 (by definition)

nair = 1.00 (to 2 decimal places)

nwater = 1.33

nglass ~ 1.5 (depending on the composition of glass)

Snell’s lawFor a ray passing from air into a medium of refractive index n, the angle of incidence i and the angle of refraction r are related by:

n =sin isin r

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Snell’s lawWhen a ray passes from one medium to another, the refractive index can be calculated using the equations:

n =

ci

cr

=nr

ni

Example

A ray of light travels from glass (ni = 1.5) into water (nr = 1.33) with an angle of incidence i of 30o. Calculate the angle of refraction r.Step 1: calculate the relative refractive index from the values for the two materials:

n =

nr

ni

=1.33 1.5

= 0.887

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Step 2: Substitute values into the Snell’s law equation, rearrange and solve:

n = sin isin r

so 0.887 =

sin 30o

sin r

sin r =

sin 30o

0.887= 0.504

so r = 34o

Questions:

1. Does a ray speed up or slow down when it enters a more dense medium?

2. If the angle between the incident ray and the reflective surface of a mirror is 35o, what are the angles of incidence and refraction?

3. A ray of light, travelling through air, strikes a glass surface with an angle of incidence of 40o. The refractive index of glass is 1.47. draw a diagram to show the situation. Calculate the angle of refraction.