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  Section: Algae » Working with Light
 
 
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Reflection

 
     
 
Content
Working with Light
  What is Light?
  How Light Behaves
    - Scattering  
    - Absorption: Lambert–Beer Law
    - Interference
    - Reflection 
    - Refraction: Snell’s Law
    - Dispersion
    - Diffraction


REFLECTION
Reflection results when light is scattered in the direction opposite to that of incident light. Light reflecting off a polished or mirrored flat surface obeys the law of reflection: the angle between the incident ray and the normal to the surface (θI) is equal to the angle between the reflected ray and the normal (θR). This kind of reflection is termed specular reflection. Most hard polished (shiny) surfaces are primarily specular in nature. Even transparent glass specularly reflects a portion of incoming light. Diffuse reflection is typical of particulate substances like powders. If you shine a light on baking flour, for example, you will not see a directionally shiny component. The powder will appear uniformly bright from every direction. Many reflections are a combination of both diffuse and specular components, and are termed spread (Figure 5.5), such as that performed by Emiliana blooms.

Now we will turn attention to the topic of curved mirrors, and specifically curved mirrors that have the shape of spheres, the spherical mirrors. Spherical mirrors can be thought of as a portion of a sphere that was sliced away and then silvered on one of the sides to form a reflecting surface. Concave mirrors were silvered on the inside of the sphere and convex mirrors were silvered on the outside of the sphere (Figure 5.6). If a concave mirror were thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror. This line is known as the principal axis. The center of sphere from which the mirror was sliced is known as the center of curvature of the mirror. The point on the mirror’s surface where the principal axis meets the mirror is known as the vertex. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is the focal point.
 
Different types of reflection: θI angle of incidence and θR angle of reflection.
FIGURE 5.5 Different types of reflection: θI angle of incidence and θR angle of reflection.

Curved mirrors: c, center of curvature of the mirror; v, vertex or geometric center of the mirror; f, focal point; r, radius of curvature; and fl, focal length.
FIGURE 5.6 Curved mirrors: c, center of curvature of the mirror; v, vertex or geometric center of the mirror; f, focal point; r, radius of curvature; and fl, focal length.

The distance from the vertex to the center of curvature is known as the radius of curvature. The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length. The focal point is the point in space at which light incident towards the mirror and traveling parallel to the principal axis will meet after reflection. In fact, if some light from the Sun was collected by a concave mirror, then it would converge at the focal point. Because the Sun is at such a large distance from the Earth, any light ray from the sun that strikes the mirror will essentially be traveling parallel to the principal axis. As such, this light should reflect through the focal point.

Unlike concave mirror, a convex mirror can be described as a spherical mirror with silver on the outside of the sphere. In convex mirrors, the focal point is located behind the convex mirror, and such a mirror is said to have a negative focal length value. A convex mirror is sometimes referred to as a diverging mirror due to its ability to take light from a point and diverge it. Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in a manner that its extension will pass through the focal point. Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.

REFRACTION: SNELL’S LAW
Refraction results when light is scattered in the same direction as that of incident light but passing between dissimilar materials, the rays bend and change velocity slightly. Refraction is dependent on two factors: the incident angle θ, that is, the angle between the incident light and the normal to the surface, and the refractive index, n of the material, defined as the ratio between the velocity of the wave in vacuum (cv) and the velocity of the wave in the medium (cs),

(5.2)

The refraction results in the following relationship

(5.3)

where 1n2 is the refracting index in passing from Medium 1 to Medium 2 and θ1 and θ2 are the angles made between the direction of the propagated waves and the normal to the surface separating the two media.

For a typical air–water boundary, (nair = 1, nwater = 1.333), a light ray entering the water at 45° from normal travels through the water at 32,11° (Figure 5.7).


Refraction of a light ray passing from a medium with lower refraction index (air) to a medium θ1, angle of incidence and θ2, angle of refraction.
FIGURE 5.7 Refraction of a light ray passing from a medium with lower refraction index (air) to a medium θ1, angle of incidence and θ2, angle of refraction.

The index of refraction decreases with increasing the wavelength. This angular dispersion causes blue light to refract more than red, causing rainbows and prisms to separate the spectrum (dispersion). Table 5.2 shows the refraction index of some common materials.

DISPERSION
Dispersion is a phenomenon that causes the separation of a light into components with different wavelenghts, due to their different velocities in a medium other than vacuum. As a consequence, the white light traveling through a triangular prism is separated into its color components, the spectrum of light. The red portion of the spectrum deviates less than the violet from the direction of propagation of the white light (Figure 5.8).

Dispersion of white light through a prism: the red portion of the spectrum deviates less than the violet from the direction of propagation of white light.
FIGURE 5.8 Dispersion of white light through a prism: the red portion of the spectrum deviates less than the violet from the direction of propagation of white light.


DIFFRACTION
Light waves change the progagation direction when they encounter an obstruction or edge, such as a narrow aperture or slit (Figure 5.9). Diffraction depends on both wavelength of incoming radiation (λ) and obstruction or edge dimensions (a). It is negligible when a/λ is sufficiently large, and becomes more and more important when the ratio tends to zero. This effect is almost absent in most optical systems, such as photographic and video cameras, with a large a/λ; but it is very important in all microscopes, where diffraction limits the resolution that microscope can ultimately achieve (a/λ tends to zero). The resolution is the smallest distance between two points to discriminate them as separate.
 
Diffraction of light from different width aperture; the effect increases with decreasing aperture width.
FIGURE 5.9 Diffraction of light from different width aperture; the effect increases with decreasing aperture width.

 
     
 
 
     




     
 
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