Reflection

Reflection coefficient

Normal Reflection Coefficient

The reflectivity of light from a surface depends upon the angle of incidence and upon the plane of polarization of the light. The general expression for reflectivity is derivable from Fresnel's Equations. For purposes such as the calculation of reflection losses from optical instruments, it is usually sufficient to have the reflectivity at normal incidence. This normal incidence reflectivity is dependent upon the indices of refraction of the two media.

For light from a medium of index   
Normally incident upon a medium of index   

The reflectivity is

This calculation of the transmission is not exactly correct since it neglects the contribution from multiple internal reflections in the medium. Since this contribution is proportional to the square and higher powers of the reflection coefficient, it can often be neglected. The reflection loss at a single surface may seem small, but with multiple lenses, it becomes an unacceptable loss. Anti-reflection coatings are used to diminish the losses.

Total Internal Reflection

When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle θc, and for incident angles greater than the critical angle there will be total internal reflection.

The critical angle can be calculated from Snell's law by setting the refraction angle equal to 90°. Total internal reflection is important in fiber optics and is employed in polarizing prisms.

For any angle of incidence less than the critical angle, part of the incident light will be transmitted and part will be reflected. The normal incidence reflection coefficient can be calculated from the indices of refraction. For non-normal incidence, the transmission and reflection coefficients can be calculated from the Fresnel equations.

Fiber Optics

The field of fiber optics depends upon the total internal reflection of light rays traveling through tiny optical fibers. The fibers are so small that once the light is introduced into the fiber with an angle within the confines of the numerical aperture of the fiber, it will continue to reflect almost losslessly off the walls of the fiber and thus can travel long distances in the fiber. Bundles of such fibers can accomplish imaging of otherwise inaccessible areas.

Mirrors in Imaging

Mirrors are used widely in optical instruments for gathering light and forming images since they work over a wider wavelength range and do not have the problems of dispersion which are associated with lenses and other refracting elements.

Mirror Instruments

Mirrors are widely used in telescopes and telephoto lenses. They have the advantage of operating over a wider range of wavelengths, from infrared to ultraviolet and above. They avoid the chromatic aberration arising from dispersion in lenses, but are subject to other aberrations. Instruments which use only mirrors to form images are called catoptric systems, while those which use both lenses and mirrors are called catadioptric systems (dioptric systems being those with lenses only).

Light Absorption

Light passing through an optical system can be attenuated by absorption and by scattering. The exponential law of absorption is the basic working relationship, but specific terms such as absorbance, absorptivity, and transmittance are widely used.

The differential absorption can be expressed as

This upon integration from 0 to x gives the exponential law of absorption:

If the absorbing medium is a solution, the concentration c is included and the law becomes

Polarization by Reflection

Since the reflection coefficient for light which has electric field parallel to the plane of incidence goes to zero at some angle between 0° and 90°, the reflected light at that angle is linearly polarized with its electric field vectors perpendicular to the plane of incidence. The angle at which this occurs is called the polarizing angle or the Brewster angle. At other angles the reflected light is partially polarized. From Fresnel's equations it can be determined that the parallel reflection coefficient is zero when the incident and transmitted angles sum to 90°. The use of Snell's law gives an expression for the Brewster angle.