The Nature of Light and Laws of Geometrical Optics

Speed of LightThe Ray approximationReflection and RefractionTotal Internal ReflectionDispersion and PrismHuygen’s PrincipleFermat’s principle

The Nature of Light

Wave front: describes wave propagation

Source Wave fronts

Rays

Rays

Wave fronts

Light is an electromagnetic wave. When emitted or absorbed, it also shows particle properties. It is emitted by accelerated electric charges.

The speed of light is a fundamental physical constant = 2.9792458x108m/s

A wave front is a surface of constant phase; wave fronts move with a speed equal to the propagation speed of the wave. A ray is a line along the direction of propagation, perpendicular to the wave fronts. Representation of light

by rays is the basis of geometric optics.

Geometric optics: the branch of optics which use the ray description.Physical optics: the branch dealing specifically with wave behavior

© 2005 Pearson Education

Reflection

ar

law of reflection

bbaa nn sinsin

law of refraction

© 2005 Pearson Education

v

cn Index of

refraction

Angles of incidence, reflection, and refraction are always measured from the normal to the surface.

Reflection and Refraction

wavelength of light in a material

n0λλ

© 2005 Pearson Education

Example

The wavelength of the red light form a helium-neon laser is 633nm in air but 474nm in aqueous humor inside your eyeball. Calculate the index of refraction of the aqueous humor and the speed and frequency of the light in this substance.

ANS:0 0

88

814

9

6331.34

474

3.00 10 /2.25 10 /

1.34

2.25 10 /4.74 10

474 10

nmn

n nm

c m sv m sn

v m sf Hz

m

© 2005 Pearson Education

© 2005 Pearson Education

When light is transmitted from one material to another, the frequency of the light is unchanged, but the wavelength and wave speed can change. The index of refraction n of a material is the ratio of the speed of light in vacuum c to the speed v in the material. If λ0 is the wavelength in a

vacuum, the same wave has a shorter wavelength λ in a medium with index of refraction n. (See Example 33.2)

© 2005 Pearson Education

When a ray travels in a material of greater index of refraction na toward a material of smaller index nb, total

internal reflection occurs at the interface when the angle of incidence exceeds a critical angle crit.

Total Internal Reflection

Application of total internal reflection

© 2005 Pearson Education

Dispersion

Usually, n decreases with increasing λ.

The dependence of wave speed and index of refraction on wavelength is called dispersion

(Chromatic)

Dispersion of light by a prism

© 2005 Pearson Education

Rainbow

Eg. The Apollo 11 astronauts set up a panel of efficient corner-cube retroreflectors on the Moon’s surface. The speed of light can be found by measuring the time interval required for a laser beam to travel from the Earth, reflect from the panel, and return to the Earth. Assume this interval is measured to be 2.51 s at a station where the Moon is at the zenith and take the center-to center distance from the Earth to the Moon to be equal to 3.84 X 108 m. (a) What is the measured speed of light?(b) Explain whether it is necessary to consider the sizes of the Earth and the Moon in your calculation.Eg. A person looking into an empty container is able to see the far edge of the container’s bottom as shown in Figure P35.26a. The height of the container is h, and its width is d. When the container is completely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the container’s bottom as shown in Figure P35.26b. (a)Show that the ratio h/d is given by

(b) Assuming the container has a width of 8.00 cm and is filled with water, use the expression above to find the height of the container. (c) For what range of values of n will the center of the coin not be visible for any values of h and d?

Eg. A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 50.0°. The index of refraction of quartz is 1.455 at 600 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.Eg. Assume a transparent rod of diameter d 5 2.00 mm has an index of refraction of 1.36. Determine the maximum angle u for which the light rays incident on the end of the rod in Figure P35.39 are subject to total internal reflection along the walls ofthe rod. Your answer defines the size of the cone of acceptance for the rod.

Eg. A triangular glass prism with apex angle = 60.0° has anindex of refraction n = 1.50 (Fig. P35.37). What is the smallest angle of incidence 1 for which a light ray can emerge from the other side?

Huygens’ principle states that if the position of a wave front at one instant is known, the position of the front at a later time can be constructed by imagining the front as a source of secondary wavelets

Huygens’ Principle

Huygens’ principle – proving the law of reflection

Huygens’ principle – proving the law of refraction

FERMAT'S PRINCIPLE OF LEAST TIMEIn 1662, Pierre de Fermat proved that a ray of light passing from a rarer to a denser medium, follows the path which takes the least time. The straight line AB would not take the least time, because the ray, in this case, would be spending a larger part of its course moving more slowly in the denser medium.

(Phys.org) —Ants have long been known to choose the shortest of several routes to a food source, but what happens when the shortest route is not the fastest? This situation can occur, for example, when ants are forced to travel on two different surfaces, where they can walk faster on one surface than on the other. In a new study, scientists have found that ants behave the same way as light does when traveling through different media: both paths obey Fermat's principle of least time, taking the fastest route rather than the most direct one. Besides revealing insight into ant communities, the findings could offer inspiration to researchers working on solving complex problems in robotics, logistics, and information technology.

Read more at: http://phys.org/news/2013-04-ants-fermat-principle.html#jCp

ANTS OBEY FERMAT'S PRINCIPLE OF LEAST TIME