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# Tag Archives: latex

Ask Physics has installed the Latex server and now users can type latex code to insert complex equations to their comments or questions.

If you are not familiar with latex code, use the following site to generate the code for the equation that you need.

http://www.codecogs.com/latex/eqneditor.php

When you visit the above site you can edit and view the result of the code generate. You have the option to copy the image of the equation or to copy the code itself (what you typed for getting the image equation; not the html code supplied) and paste the code in your comment.

Go, Try it Now! $(a+b)^{2}=a^{2}+b^{2}+2ab$

## How light maintain its speed after refraction?

How light maintain its speed after refraction? -(Naveen Saxena asked)

The speed of light in a medium is constant. When light enters from one medium to another, there is a change in the speed of light and the change is almost instantaneous. The speed of light in a medium depends on the electric and magnetic properties of the medium, more specifically, the electric permitivity and magnetic permeability of the medium.

The speed of light in a medium is given by $(a+b)^{2}=a^{2}+b^{2}+2ab$

Wikipedia says

“At the microscale, an electromagnetic wave’s phase speed is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be “shaken” back and forth at the same frequency. The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay, as the charges may move out of phase with the force driving them . The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: The original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave’s phase speed. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies .

Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:

• If the electrons emit a light wave which is 90° out of phase with the light wave shaking them, it will cause the total light wave to travel more slowly. This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.
• If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the total light wave to travel more quickly. This is called “anomalous refraction”, and is observed close to absorption lines, with X-rays, and in some microwave systems. It corresponds to a refractive index less than 1. (Even though the phase velocity of light is greater than the speed of light in vacuum c, the signal velocity is not, as discussed above). If the response is sufficiently strong and out-of-phase, the result is negative refractive index discussed below.
• If the electrons emit a light wave which is 180° out of phase with the light wave shaking them, it will destructively interfere with the original light to reduce the total light intensity. This is light absorption in opaque materials and corresponds to an imaginary refractive index.
• If the electrons emit a light wave which is in phase with the light wave shaking them, it will amplify the light wave. This is rare, but occurs in lasers due to stimulated emission. It corresponds to an imaginary index of refraction, with the opposite sign as absorption.

For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption.”

## de Broglie Wavelength

Alpha particle and a proton are accelerated from rest by the same potential. Find the ratio of their de- broglie wavelength

Charge of alpha particle = 2e

Mass of alpha particle = 4 u

Charge of proton = e

mass of proton = u

The energy acquired by proton when accelerated through a pd of V,

E=eV

The momentum acquired by proton= $(a+b)^{2}=a^{2}+b^{2}+2ab$

The de Broglie wavelength is given by $(a+b)^{2}=a^{2}+b^{2}+2ab$

Therefore, de Broglie wavelength of Proton, $(a+b)^{2}=a^{2}+b^{2}+2ab$

Similarly, $(a+b)^{2}=a^{2}+b^{2}+2ab$ $(a+b)^{2}=a^{2}+b^{2}+2ab$

## Problem from relative velocity

A Boat covers certain distance between two spots in a river taking t1 hrs going downstream and t2 hrs going upstream. What time will be taken by boat to cover same distance in still water?

posted by STUTI $t=\frac{2t_{1}t_{2}}{t_{1}+t_{2}}$

## A question from Kinematics : 100m long a train passing a 40m long bridge in 20.Find out the velocity of the train?

Mitu asked – “100m long a train passing a 40m long bridge in 20.Find out the velocity of the train?”

Ans: The total distance to be traveled by the train to completely traverse the bridge is 100 + 40 = 140 m

Time = 20 s

From the relation, $speed = \frac{distance}{time}$ $speed = \frac{140}{20}=7m/s$

## Equations of Motion – Images for easy reuse

Here you can find the equations of motion in the form of images which you can use in your documents. $v = u + at$ $S = ut + \frac{1}{2} at^{2}$ $v^{2} = u^{2} + 2aS$

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