Matlab code for vector format of Snell law please

Given a unit vector(in air for example) and a given unit Normal vector(normal of flat water)

Can I get please a code for calculating the vector after refraction(Snell law).

All in 3D

Help would be very welcome.

Answer 1

[Aby]

% Define input parameters
unit_vector = [1, 0, 0]; % Example incident unit vector
normal_vector = [0, 0, 1]; % Example normal vector
n1 = 1; % Refractive index of air
n2 = 1.5; % Refractive index of water

% Call the function to calculate the refracted vector
refracted_vector = snells_law(unit_vector, normal_vector, n1, n2);

% Display the result
disp('Refracted Vector:');
disp(refracted_vector);

function refracted_vector = snells_law(unit_vector, normal_vector, n1, n2)
    % n1: refractive index of the initial medium
    % n2: refractive index of the medium being entered into
    
    % Ensure that the input vectors are unit vectors
    unit_vector = unit_vector / norm(unit_vector);
    normal_vector = normal_vector / norm(normal_vector);
    
    % Calculate the dot product of the unit vector and the normal vector
    cos_theta1 = dot(-unit_vector, normal_vector);
    
    % Calculate the sine of the angle of incidence
    sin_theta1 = sqrt(1 - cos_theta1^2);
    
    % Calculate the sine of the angle of refraction using Snell's law
    sin_theta2 = (n1 / n2) * sin_theta1;
    
    % If the value inside sqrt is negative, total internal reflection occurs
    if sin_theta2 > 1
        fprintf('Total internal reflection occurs.\n');
        refracted_vector = NaN;
    else
        % Calculate the cosine of the angle of refraction
        cos_theta2 = sqrt(1 - sin_theta2^2);
        
        % Calculate the refracted vector using Snell's law
        refracted_vector = (n1 / n2) * unit_vector + ((n1 / n2) * cos_theta1 - cos_theta2) * normal_vector;
        
        % Normalize the refracted vector to ensure it remains a unit vector
        refracted_vector = refracted_vector / norm(refracted_vector);
    end
end