The law of reflection states that the angle of reflection equals the angle of incidence. Formulate the relationship between the angle of reflection and the angle of incidence
We expect to see reflections off a smooth surface. However, light strikes different parts of a rough surface at different angles, and it is reflected in many different directions ("diffused"). Diffused light is what allows us to see a sheet of paper from any angle. Many objects, such as people, clothing, leaves, and walls, have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth surface (compared with the wavelength of light) and reflects light at specific angles. When the moon reflects off the surface of a lake, a combination of these effects takes place. Reflection: A brief overview of reflection and the law of reflection. The amount that a light ray changes its direction depends both on the incident angle and the amount that the speed changes. Formulate the relationship between the index of refraction and the speed of light
Refraction: The changing of a light ray's direction (loosely called bending) when it passes through variations in matter is called refraction. The speed of light c not only affects refraction, it is one of the central concepts of Einstein's theory of relativity. The speed of light varies in a precise manner with the material it traverses. It makes connections between space and time and alters our expectations that all observers measure the same time for the same event, for example. The speed of light is so important that its value in a vacuum is one of the most fundamental constants in nature as well as being one of the four fundamental SI units. Why does light change direction when passing from one material ( medium ) to another? It is because light changes speed when going from one material to another. A ray of light changes direction when it passes from one medium to another. As before, the angles are measured relative to a perpendicular to the surface at the point where the light ray crosses it. The change in direction of the light ray depends on how the speed of light changes. The change in the speed of light is related to the indices of refraction of the media involved. In mediums that have a greater index of refraction the speed of light is less. Imagine moving your hand through the air and then moving it through a body of water. It is more difficult to move your hand through the water, and thus your hand slows down if you are applying the same amount of force. Similarly, light travels slower when moving through mediums that have higher indices of refraction. The amount that a light ray changes its direction depends both on the incident angle and the amount that the speed changes. For a ray at a given incident angle, a large change in speed causes a large change in direction, and thus a large change in angle. The exact mathematical relationship is the law of refraction, or "Snell's Law," which is stated in equation form as: n1sinθ1 = n2sinθ2 Here n1 and n2 are the indices of refraction for medium 1 and 2, and θ1 and θ2 are the angles between the rays and the perpendicular in medium 1 and 2. The incoming ray is called the incident ray and the outgoing ray the refracted ray, and the associated angles the incident angle and the refracted angle. The law of refraction is also called Snell's law after the Dutch mathematician Willebrord Snell, who discovered it in 1621. Snell's experiments showed that the law of refraction was obeyed and that a characteristic index of refraction n could be assigned to a given medium. Understanding Snell's Law with the Index of Refraction: This video introduces refraction with Snell's Law and the index of refraction.The second video discusses total internal reflection (TIR) in detail. Total internal reflection happens when a propagating wave strikes a medium boundary at an angle larger than a particular critical angle. Formulate conditions required for the total internal reflection
What is Total Internal Reflection?: Describes the concept of total internal reflection, derives the equation for the critical angle and shows one example. θc\theta_\text{c}θc is given by Snell's law,n1sinθ1=n2sinθ2\text{n}_1\sin\theta_1 = \text{n}_2\sin\theta_2n1sinθ1=n2sinθ2 . Here, n1 and n2 are refractive indices of the media, andθ1\theta_1θ1 andθ2\theta_2θ2 are angles of incidence and refraction, respectively. To find the critical angle, we find the value forθ1\theta_1θ1 whenθ2\theta_2θ2 = 90° and thussinθ2=1\sin \theta_2 = 1sinθ2=1 . The resulting value ofθ1\theta_1θ1 is equal to the critical angleθc=θ1=arcsin(n2n1)\theta_\text{c} = \theta_1 = \arcsin \left( \frac{\text{n}_2}{\text{n}_1} \right)θc=θ1=arcsin(n1n2) . So the critical angle is only defined when n2/n1 is less than 1.Total internal reflection is a powerful tool since it can be used to confine light. One of the most common applications of total internal reflection is in fibre optics. An optical fibre is a thin, transparent fibre, usually made of glass or plastic, for transmitting light. The construction of a single optical fibre is shown in.
Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a surface. Calculate the Brewster's angle from the indices of refraction and discuss its physical mechanism
The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to p-polarized light (whose electric field is polarized in the same plane as the incident ray and the surface normal). One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The refracted light is emitted perpendicular to the direction of the dipole moment; no energy can be radiated in the direction of the dipole moment. Thus, if the angle of reflection θ1 (angle of reflection) is equal to the alignment of the dipoles (90 - θ2), where θ2 is angle of refraction, no light is reflected. This geometric condition can be expressed as θ1+θ2=90∘\theta_1 + \theta_2 = 90 ^{\circ}θ1+θ2=90∘ , where θ1 is the angle of incidence and θ2 is the angle of refraction. Using Snell's law (n1sinθ1 = n2sinθ2), one can calculate the incident angle θ1 = B at which no light is reflected:n1sin(θB)=n2sin(90∘−θB)=n2cos(θB).\text{n}_1 \sin {\left( \theta_\mathrm {\text{B}} \right)} =\text{n}_2 \sin {\left( 90^\circ - \theta_\mathrm {\text{B}} \right)}=\text{n}_2 \cos {\left( \theta_\mathrm {\text{B}} \right)}.n1sin(θB)=n2sin(90∘−θB)=n2cos(θB). Solving for θB givesθB=arctan(n2n1).\theta_\mathrm {\text{B}} = \arctan {\left( \frac{\text{n}_2}{\text{n}_1} \right)}.θB=arctan(n1n2). When light hits a surface at a Brewster angle, reflected beam is linearly polarized. shows an example, where the reflected beam was nearly perfectly polarized and hence, blocked by a polarizer on the right picture. Polarized sunglasses use the same principle to reduce glare from the sun reflecting off horizontal surfaces such as water or road.
Dispersion is defined as the spreading of white light into its full spectrum of wavelengths. Describe production of rainbows by a combination of refraction and reflection processes
Refraction is responsible for dispersion in rainbows and many other situations. The angle of refraction depends on the index of refraction, as we saw in the Law of Refraction. We know that the index of refraction n depends on the medium. But for a given medium, n also depends on wavelength. Note that, for a given medium, n increases as wavelength decreases and is greatest for violet light. Thus violet light is bent more than red light and the light is dispersed into the same sequence of wavelengths. Rainbows are produced by a combination of refraction and reflection. You may have noticed that you see a rainbow only when you look away from the sun. Light enters a drop of water and is reflected from the back of the drop. The light is refracted both as it enters and as it leaves the drop. Since the index of refraction of water varies with wavelength, the light is dispersed, and a rainbow is observed. (There is no dispersion caused by reflection at the back surface, since the law of reflection does not depend on wavelength. ) The actual rainbow of colors seen by an observer depends on the myriad of rays being refracted and reflected toward the observer's eyes from numerous drops of water. The arc of a rainbow comes from the need to be looking at a specific angle relative to the direction of the sun.
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