Application Design of Newton-Rapshon method in Proving Maximum Wavelength on Wien’s Displacement Law

Abstract

The Calculation of the maximum wavelength (?m) of radiation emitted by a black body can be determined from the Wien displacement law, which states the ratio between the Wien constant and the absolute temperature (T). Wien's displacement law can be derived analytically from the Energy Density equation (U?) in Plank's law. The solution for U? is obtained by calculating the first derivative of the function with respect to ? or dU?/d?, and then proceeding with finding a solution to the equation for the derivative. The solution of dU?/d? is the value of ? that makes dU?/d? equal to zero. The resulting wavelength is the maximum wavelength ?m, which is the wavelength value that makes the value in the equation U? the maximum value. The final result of this calculation is the Wien’s displacement law, namely the multiplication of ?m with T equals the Wien constant. So basically, the derivation of Wien's displacement law is to find the maximum value of the function f(x). The maximum value of the function f(x) can be done numerically. Solving numerically can be done with the Modified Newton-Rapshon method. The modified Newton-Rapshon method is usually implemented in the form of computer program code. In this research, the results of the calculation of the maximum wavelength ?m analytically are very close to the results of numerical calculations (modified NR). This can be seen from the results of linear regression with gradient values (m), regression constants (c) and coefficient of determination (R2) close to the ideal values of 1, 0 and 1, respectively.