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Introduction to reflection and refraction

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Introduction to reflection and refraction

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  • October 11, 2006
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1.1 Introduction

This "book" is not intended to be a vast, definitive treatment of everything that is known

about geometric optics. It covers, rather, the geometric optics of first-year students,

whom it will either help or confuse yet further, though I hope the former. The part of

geometric optics that often causes the most difficulty, particularly in getting the right

answer for homework or examination problems, is the vexing matter of sign conventions

in lens and mirror calculations. It seems that no matter how hard we try, we always get

the sign wrong! This aspect will be dealt with in Chapter 2. The present chapter deals

with simpler matters, namely reflection and refraction at a plane surface, except for a

brief foray into the geometry of the rainbow. The rainbow, of course, involves refraction

by a spherical drop. For the calculation of the radius of the bow, only Snell's law is

needed, but some knowledge of physical optics will be needed for a fuller understanding

of some of the material in section 1.7, which is a little more demanding than the rest of

the chapter.

1.2 Reflection at a Plane Surface

The law of reflection of light is merely that the angle of reflection r is equal to the angle

of incidence r. There is really very little that can be said about this, but I'll try and say

what little need be said.

i. It is customary to measure the angles of incidence and reflection from the normal to

the reflecting surface rather than from the surface itself.

i r

FIGURE I.1

2

ii. Some curmudgeonly professors may ask for the lawS of reflection, and will give you

only half marks if you neglect to add that the incident ray, the reflected ray and the

normal are coplanar.

iii. A plane mirror forms a virtual image of a real object:

or a real image of a virtual object:

FIGURE I.2

• O I °

FIGURE I.3

• I O °

3

iv. It is usually said that the image is as far behind the...