Introduction to Light IN THIS LECTURE –Reflection and refraction –Index of refraction –Snell’s Law –Critical Angle –Dispersion and refractive index –Interference phenomena –Retardation

Reflection Light reaching the boundary between two transparent materials may either be reflected or refracted. For reflected light the angle of incidence (i) and the angle of reflection (r) are identical Mineral lustre depends in part on the amount of light that is reflected from the surface. In general the amount of light reflected at a surface increases as the angle of incidence increases

Refraction Wave fronts one wavelength apart and the wave normal are shown for light rays passing from material 1 (low index of refraction, higher velocity) to material 2 (high index of refraction, low velocity). The wave fronts and wave normal are bent at the interface because the wavelength 2 in low-velocity material is shorter than the wavelength 1 in the high- velocity material.

Index of Refraction A measure of how effective a material is in bending light is called the Index of Refraction (n), which is a function of velocity Index of Refraction in Vacuum = 1 and for all other materials n > 1.0. The velocity of light in most minerals is in the range 2 – 1.4 x nm/sec. Therefore most minerals have n values in the range 1.4 to 2.0. A high refractive index indicates a low velocity for light travelling through that particular medium. n = V v / V m where Vv is the velocity in a vacuum and Vm is the velocity in a material

Snell's law can be used to calculate how much light is bent on travelling from medium one to medium two. If the interface between the two materials represents the boundary between air (n ~ 1) and water (n = 1.33) and if angle of incidence = 45°, using Snell's Law the angle of refraction = 32°. The equation holds whether light travels from air to water, or water to air. In general, the light is refracted towards the normal to the boundary on entering the material with a higher refractive index and is refracted away from the normal on entering the material with lower refractive index. Snell’s Law sin  1 sin  2 = n2n2 n1n1

Critical Angle Light following wave normals a, b and c within the white arc can be refracted from the high-index to the low index materials because their angle of incidence is less than the critical angle (CA). Wave normals such as d, which have an angle of incidence greater than the critical angle are totally reflected to d' at the boundary. A portion of the light following wave normals a, b and c is reflected to a', b' and c' as shown with dotted lines. The amount of reflection increases from a to c and is 100% for angles of incidence greater than the CA. If the indices of refraction are known then the critical angle can be calculated as from -> n 1 (low) n 2 (high) = sin CA

Dispersion White light is dispersed into its spectral colors when passed through a prism because the index of refraction for violet light is larger than for red light Therefore the index of refraction is higher for short wavelengths and lower for long wavelengths of light This relationship is known as the normal dispersion of the refractive indices

Dispersion and Refractive Index For the normal dispersion of the refractive indices, the index of refraction decreases with increasing wavelength. To describe the dispersion of a particular material it is necessary to report the index of refraction at several wavelengths. By convention indices of refraction nF, nD and nC are reported for light whose wavelengths are 486, 589 and 656nm respectively. When a single index of refraction is reported it is normally nD because 589 light is in the middle of the visible spectrum and is easily reproduced by a sodium lamp in a laboratory.

Interference Phenomena For isotropic minerals all light is absorbed by the upper polariser and the mineral appears dark (we will look at how optical microscopes work in more detail later) For anisotropic minerals, light entering the mineral is split into two rays that vibrate at right angles to each other and have different indices of refraction (ie different velocities) Because the two different rays have different velocities they travel at different speeds through the mineral. The light ray with the lower velocity is called the slow ray, the ray with the higher velocity is called the fast ray.

Retardation RETARDATION (  ) represents the distance the fast ray has travelled once leaving the mineral before the slow ray also leaves the mineral. Retardation is measured in nanometres, 1nm = 10-7cm, or the number of wavelengths by which a wave lags behind another light wave. Retardation remains constant once the two rays have left the mineral because their velocities in air will be the same. Retardation can result in light rays Constructively interfering Destructively interfering Partially interfering

Constructive Interference Waves A and B are in phase (  = 1 ) so that the waves constructively interfere and produce the resultant wave R

Destructive Interference Waves A and B are out of phase (  = 1 + 1/2 ). The amplitude of waves A and B are equal but opposite such that they cancel each other out (destructively interfere). The resultant wave R therefore has zero amplitude.

Partial Interference Waves A and B are partially in phase with the interference being partially constructive and partially out of phase with the interference being partially destructive. The resultant wave R is the sum of waves A and B at any given point.