1.1 Refraction and Reflection

1.1.1 Refraction

When a light ray strikes a smooth interface between two transparent media at an angle,it is refracted.Each medium may be characterized by an index of refraction n, which is a useful parameter for describing the sharpness of the refraction at the interface.The index of refraction of air(more precisely,of free space) is arbitrarily taken to be one, n is most conveniently regarded as a parameter whose value is determined by experiment.We know now that the physical significance of n is that the ratio of the velocity of light in vacuo to that in the medium.

Suppose that the ray is incident on the interface,as shown in Fig.1.1.It is refracted in such a way that

no matter what the inclination of the incident ray to the surface,n is the index of refraction of the first medium, n′ that of the second.The angle of incidence i is the angle between the incident ray and the normal to the surface;the angle of refraction i′ is the angle between the refracted ray and the normal.

1.1.2 Index of Refraction

Most common optical materials are transparent in the visible region of the spectrum, whose wavelength ranges from 400 to 700nm. They exhibit strong absorption at shorter wavelengths, usually 200nm and below.

The refractive index of a given material is not independent of wavelength, but generally increases slightly with decreasing wavelength (Near the absorption edge at 200 nm, the index of glass increases sharply). This phenomenon is known as dispersion. Dispersion can be used to display a spectrum with a prism; it also gives rise to unwanted variations of lens properties with wavelength.Table 1.1 gives typical index of refraction of several materials.

Optical glasses are generally specified both by index n and by a quantity known as dispersion v,

The subscripts F,D and C refer to the indexes at certain short,middle and long wavelengths(blue, yellow,red).

1.1.3 Reflection

Certain highly polished metal surfaces and other interfaces may reflect all or nearly all of the light falling on the surface. In addition, ordinary, transparent glasses reflect a few percent of the incident light and transmit the rest.

The angle of incidence is i and the angle of reflection i′. Experiment shows that the angles of incidence and reflection are equal,except in a very few peculiar cases,as shown in Fig.1.2.

We shall later adopt the convention that i is positive;that is,if the acute angle opens counterclockwise from the normal to the ray, i is positive. The sign of i′ is clearly opposite to that of i. We therefore write the law of reflection as

1.1.4 Total Internal Reflection

Here we consider a ray that strikes an interface from the high-index side,say,from glass to air (not air to glass).This is known as internal reflection.The law of refraction shows that the incident

parallel to the interface.In this case, i′ =90°,so the law of ray is in this case bent away from the normal when it crosses the interface,as shown in Fig.1.3.Thus,there will be some angle of incidence for which the refracted ray will travel just refraction becomes

where ic is known as the critical angle.Since sin 90°=1,

If i exceeds ic,then nsini＞n′,and the law of refraction

demands that sin i′ exceed 1.Because this is impossible,we can conclude only that there can be no refracted ray in such cases.The light cannot simply vanish,so we are not surprised that it must be wholly reflected;this is indeed the case.The phenomenon is known as total internal reflection;it occurs whenever

The reflected light,of course,obeys the law of reflection.

For a typical glass-air interface, n=1.5, the critical angle is about 42°. Glass prisms that exhibit total reflection are therefore commonly used as mirrors with angles of incidence of about 45°.

1.1.5 Reflecting Prisms

There are different types of reflecting prism. The most common are prisms whose cross sections are right isosceles triangles.One advantage of a prism over a metal-coated mirror is that its reflectance is nearly 100% if the surfaces normal to the light are antireflection coated. Further, the prism’s properties do not change as the prism ages, whereas metallic mirrors are subject to oxidation and are relatively easy to scratch. A glass prism is sufficiently durable that it can withstand all but the most intense laser beams. Fig.1.4 shows a prism being used in place of a plane mirror.

In imaging-forming systems, these prisms must be used in collimated light beams to avoid introducing defects into the optical image.