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How can one derive the dispersion relation for a given physical system?

To derive the dispersion relation for a physical system, one typically starts with the equations that describe the system's behavior, such as wave equations or equations of motion. By analyzing these equations and applying mathematical techniques like Fourier transforms or solving for the system's eigenvalues, one can determine the relationship between the system's frequency and wavevector, known as the dispersion relation. This relation helps understand how waves propagate through the system and how different frequencies and wavelengths are related.


An object is placed between focus and centre of curvature of a concave mirror. Draw a ray diagram and derive mirror formula. Also write magnification formula.?

In a concave mirror, when an object is placed between the focus and the center of curvature, the image formed is real, inverted, and enlarged. To derive the mirror formula, use the mirror formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. The magnification formula is: M = -v/u, where M is the magnification, v is the image distance, and u is the object distance.


How do you derive joule's law?

Joule's law, which states the relationship between electrical power, current, and resistance, is derived from Ohm's law, P = IV, and the formula for electrical power, P = I^2R. By substituting I = V/R from Ohm's law into the power formula, you can derive Joule's law as P = V^2/R.


What do you mean by critical velocity by method of dimensions establish its relation?

Critical velocity is the minimum velocity required for an object to overcome a particular resistance force. By using the method of dimensions, you can establish a relationship between critical velocity and the factors that influence it, such as the viscosity of the fluid, density of the fluid, and the size and shape of the object. By analyzing the dimensions of these factors and the force equation, you can derive an equation that relates critical velocity to these variables.


How can you derive the formula for force (F) using the equation fma, which relates force (F), mass (m), and acceleration (a)?

To derive the formula for force (F) using the equation fma, you can rearrange the equation to solve for force. By dividing both sides of the equation by mass (m), you get F ma, where force (F) is equal to mass (m) multiplied by acceleration (a). This formula shows the relationship between force, mass, and acceleration.

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Both live together to derive benefit from each other.


How can you Derive relation between 1 coulomb stat coulomb?

1 coulomb= 3*109 statcoulomb


How do you derive relation between focal length and radius of curvature of concave mirror?

Consider a ray of light AB, parallel to the principal axis, incident on a spherical mirror at point B. The normal to the surface at point B is CB and CP = CB = R, is the radius of curvature. The ray AB, after reflection from mirror will pass through F (concave mirror) or will appear to diverge from F (convex mirror) and obeys law of reflection, i.e., i = r. From the geometry of the figure, If the aperture of the mirror is small, B lies close to P, BF = PF or FC = FP = PF or PC = PF + FC = PF + PF or R = 2 PF = 2f or F=R/2 or 2F=R Hope this helps............


How do you derive scattering matrix?

s=b/a for n port network in matrix form[b]=[s]*[a].there is also relation between z matrix in s matrix.


How do you Derive The Number of Transitive relation of a Set 's' having n elements?

vbvb


How can one derive the dispersion relation for a given physical system?

To derive the dispersion relation for a physical system, one typically starts with the equations that describe the system's behavior, such as wave equations or equations of motion. By analyzing these equations and applying mathematical techniques like Fourier transforms or solving for the system's eigenvalues, one can determine the relationship between the system's frequency and wavevector, known as the dispersion relation. This relation helps understand how waves propagate through the system and how different frequencies and wavelengths are related.


An object is placed between focus and centre of curvature of a concave mirror. Draw a ray diagram and derive mirror formula. Also write magnification formula.?

In a concave mirror, when an object is placed between the focus and the center of curvature, the image formed is real, inverted, and enlarged. To derive the mirror formula, use the mirror formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. The magnification formula is: M = -v/u, where M is the magnification, v is the image distance, and u is the object distance.


How to derive the centre of curvature?

This involves the rate of change of the unit tangent vector. Deriving the curvature starts with the equation of a circle. Then three equations that force the collocation circle to go through the three points and on the curve must be written down. Then solve for a, b, and r.


Where does the term olympiad derive from?

How long between each Olympics


How do you Derive The Number of symetric relation of a Set 's' having n elements?

2^(n^2+n)/2 is the number of symmetric relations on a set of n elements.


What is inferential relation?

An inferential relation refers to the connection between premises and conclusions in reasoning, where the truth of the premises supports the likelihood or plausibility of the conclusion. This relationship is central to inductive reasoning, where generalizations are made based on specific observations. In contrast, deductive reasoning establishes a definitive conclusion based on established premises. Essentially, inferential relations help us derive insights or predictions from available information.


Derive the castiglinos theorem?

Derive the castiglino's theorem