V-Lab @ ANDC

Newton-Rapson-Method

For finding the roots of linear, quadratic and third degree polynomial.

For finding the roots of transcendental equation.

Given a function f(x) on floating number x and an initial guess for root, find root of function in interval. Here f(x) represents algebraic or transcendental equation. For simplicity, derivative of function is also provided. Example:
Input:
A function of x (for example x3 +4x2 + 8.),
derivative function of x (3x2 +8x) and an initial guess x0 = -1
Output:
The value of root is : -4.412 or any other value close to root.

f(x)= a x3 +b x2+c x1 + d :

Enter the coefficients of the equation:

x3+ x2+ x1+

x0 =
Result:

Given a function f(x) on floating number x and an initial guess for root, find root of function in interval. Here f(x) represents transcendental equation. For simplicity, derivative of function is also provided. Example:
Input:
A function of x (for example= x2 -2sinx),
derivative function of x = 2(x-cosx) and an initial guess x0 = 2
Output:
The value of root is : 1.405 or any other value close to root.

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object (in the far-field region), and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the object (in the near field region) is given by the Fresnel diffraction equation.
Fraunhofer-diffraction Fraunhofer-diffraction
By using the intensity equation I/I0= (sinx/x)2,maxima or minima is calculated accordingly. Here the value of x is founded by solving the equation (x-tanx) and finding its different roots.

f(x)= x-tanx

x0 =

Result: Root of the eqation is
**Enter the value of roots in ascending order.
Value of Root Value of intensity I/I0