#### Reflection and Refraction of Light, Physics tutorial

Light (or optics) is a form of energy that causes the sensation of vision. This energy relationship with light is termed as luminous energy and it is the energy that causes the sensation of vision if it falls on our eyes.

Reflection of Light at Plane Surfaces:

If light falls on an object, a few of it bounces off the object. The bouncing off of light at a surface is termed as reflection. All the surfaces reflect light. How well a surface reflects light based on the nature of the surface. Shiny, smooth surfaces like a mirror reflect light better than dull, rough surfaces like a wall or a sheet of paper.

If a beam of light falls on the smooth surface, the rays of the beam are reflected in a specific direction and remain parallel to one other. This is termed as regular reflection. As the rays are reflected in an arranged fashion, the image formed is clear.

If a beam hits an uneven surface, its rays are reflected in various directions. This is termed as diffuse reflection or irregular reflection. As the reflected rays get diffused or spread, in various directions, we observe a hazy image or no image at all.

The laws of reflection at plane surfaces are as follows:

1) Incident ray and reflected ray both lie on either sides of the normal.

2) Incident ray, Reflected ray and the normal lie in one plane that is termed as the plane of incidence.

3) Angle of incidence = Angle of reflection

i = r

Refraction of Light:

Refraction is basically the bending of waves as they pass from one medium to the other, due to a change in their speed. The phenomenon is most generally related with light, however can as well apply to sound, or even water, waves. It occurs if a series of waves travels toward the new medium at an angle, in such a way that one side undergoes a change in speed before the other, causing it to turn toward the slower side in the similar manner that a moving vehicle will tend to turn when one side is slowed more than the other. The Refraction can cause objects to appear displaced, and might amplify distant sounds. It consists of numerous uses in the context of light, like as prisms and lenses.

Refractive Index:

Each and every medium via which waves can move consists of a refractive index which points out how fast they will travel. In case of light, this is found by dividing its speed in a vacuum through its speed in that specific medium. This is a ratio between the speeds of the mediums; therefore it is not measured in any unit. The refractive index usually rises by the density of the medium: it is one for a vacuum and is more than one for all identified natural materials.

Refraction of Light through Rectangular Glass Block:

If light travels from one medium to the other, it usually bends or refracts. The law of refraction gives us a manner of predicting the amount of bend. The law is more complex than that for reflection; however an understanding of refraction will be essential for our future discussion of lenses and their applications. The law of refraction is as well termed as Snell's law, named for Willobrord Snell, who proposed the law in the year 1621.

Snell's law introduces the relationship between angles of incidence and refraction for a wave imposing on an interface between two media having different index of refraction. The law obeys from the boundary condition which a wave is continuous across a boundary that needs that the stage of the wave be constant on any particular plane, resultant in:

Snell's law:

n1sinθ1 = n2sinθ2

Or, μ = n2/n1 = sinθ1/sinθ2

Here μ is a constant termed as refractive index.

Rule 1: If a light ray travels from a rarer medium to the denser medium, the light ray bends in the direction of the normal.

Rule 2: If a light ray travels from a denser medium to a rarer medium, the light ray bends away from the normal.

Electromagnetic waves at the interface separating two media:

Assume that, there is a plane electromagnetic wave which is incident on a boundary between the two linear media. That is, D and H are proportional to E and B, correspondingly, and the constants of proportionality are independent of the position and direction. We can assume it as a light passing from air (that is, medium 1) to the glass (that is, medium 2). Let us suppose that there are no free charges or currents in the materials.

The figure above exhibits that a plane boundary between two media having dissimilar permittivity and permeability: ε1, µ1 for medium 1 and ε2, µ2 for medium 2. The uniform plane wave travelling to the right in medium 1 is incident on the interface normal to the boundary. As in the case of waves on a string, we anticipate a reflected wave propagating back to the medium and a transmitted (or refracted) wave travelling in the second medium. We want (a) to derive expressions for the fields related by the reflected and refracted waves in terms of the field related by the incident wave and (b) to recognize the fraction of the incident energy that is reflected and transmitted. To do so we require knowing the boundary conditions satisfied through these waves at the interface separating the two media. We get such conditions through stipulating that Maxwell's equations should be satisfied at the boundary between such media.

Boundary Conditions:

The integral form of the Maxwell's equations for a medium free of charges and currents is as follows:

ε∫S E. dS = 0

S B. dS = 0

C E. dI = d/dt ∫S B. dS

And (1/μ) ∫C B. dI = ε d/dt ∫S E. dS

Here 'S' is a surface bound through the closed loop C.

The electric field can oscillate either normal or parallel to the plane of the incidence. The magnetic field 'B' will then be parallel or normal to the plane of incidence. We represent these with subscripts || (parallel) and ⊥ (normal). The boundary conditions for normal and parallel components of electric and magnetic fields take the form as:

ε1 E1 - ε2 E2 = 0

B1 - B2 = 0

E1|| - E2|| = 0

And (1/μ1) B1|| - (1/μ2) B2|| = 0

We now make use of the boundary conditions represented by the above equations to study the reflection and refraction (transmission) at normal and also oblique incidence.

Idealization of Waves as Light Rays:

We are very much familiar to describe the reflection and refraction of plane electromagnetic waves at a plane interface. This represents a relatively simple condition where the solutions of Maxwell's equations present the laws of propagation of light. It is not true in common, and we perpetually seek approximations to explain a phenomenon well. One such approximation makes utilization of the smallness of the wavelength of light. We are familiar that the wavelength of light is very small (~10-7m). This is of the order of magnitude less than the dimensions of optical instruments like microscopes and telescopes. In these situations, the passage of light is most simply represented by geometrical rays. A ray is the path of propagation of energy in the zero wavelength limit (0 → λ). The manner in which the rays might stand for the propagation of wave-fronts for some familiar condition is shown below. We will notice that the plane wave-front corresponds to the parallel rays and spherical wave-fronts correspond to rays diverging from the point or converging to a point. We will agree that all the portions of the wave-front take the similar time to travel from the source.

The laws of geometrical optics are integrated in the Fermat's principle.

Fermat's Principle:

In its innovative form, the Fermat's principle might be described as follows:

Any light ray travels among the two end points all along a line requiring the minimum transit time.

If 'v' is the speed of light at a particular point in a medium, the time taken to cover the distance 'dl' is:

dt = dl/v

We are familiar that the refractive index of a medium is stated as the ratio of the speed of light in the vacuum to its speed in the medium, that is,

n = c/v

By employing this relation in the equation dt = dl/v, we get:

dt = (1/c) (n dl)

Huygens stated that the light propagates as a wavefront (that is, a surface of constant phase) progresses in a medium perpendicular to itself by means of the speed of light. The zero wavelength approximation of wave optics is termed as geometrical optics.

Therefore, the time taken by light in covering the distance from point A to B is:

τ = (1/c) AB n dl

The quantity:

L = AB n dl

Consists of the dimensions of length and is termed as the optical distance or optical path length among two given points. You should recognize that the optical distance is dissimilar from the physical (or geometrical) distance (= AB dl) though, in a homogeneous medium, the optical distance is equivalent to the product of the geometrical length and the refractive index of the medium. Therefore, we can write:

τ = L/c

This is the Format's principle of least time. Now take a moment and think: Is there any exception to this law? Yes, there are cases where the optical path corresponds to the maximum time or it is neither maximum nor minimum that is, stationary. To incorporate these conditions, this principle is tailored as follows:

Out of numerous paths joining the two given points, the light ray follows that path for which the time needed is an extreme. In other words, the optical path length between any two points is a minimum, maximum and stationary.

The vital point comprised in Fermat's principle is that the slight variation in the real path causes a second-order variation in the actual path. Let us suppose that the light propagates from point A in the medium characterized through the refractive index n to the point B. According to this principle:

δ AB n (x, y, z) dl = 0

For a homogeneous medium, the rays are straight lines, as the shortest optical path among the two points is all along a straight line.

In effect, the Fermat's principle excludes the consideration of an isolated ray of-light. It states us that a path is real only if we expand our examination to the paths in immediate neighborhood of the rays.

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