Numerical Methods

\[ \frac{1}{2} = 0.5 \]

        
% Parameters
n = 2.4; % Refractive index of the Fresnel Rhomb
theta_critical = asind(1 / n); % Critical angle in degrees
theta_incidence = linspace(theta_critical, 89.9, 1000); % Angle of incidence range

% Initialize phase difference array
delta_phi = zeros(size(theta_incidence));

% Calculate phase difference for each angle
for i = 1:length(theta_incidence)
    theta = deg2rad(theta_incidence(i)); % Convert to radians
    r_te = (cos(theta) - sqrt(n^2 - sin(theta)^2)) / ...
           (cos(theta) + sqrt(n^2 - sin(theta)^2));
    r_tm = (n^2 * cos(theta) - sqrt(n^2 - sin(theta)^2)) / ...
           (n^2 * cos(theta) + sqrt(n^2 - sin(theta)^2));
    delta_phi(i) = abs(angle(r_tm) - angle(r_te)); % Phase difference
end

% Find the angle where 2*delta_phi = pi/2
target_delta_phi = pi / 4; % Since 2*delta_phi = pi/2
[~, idx] = min(abs(2 * delta_phi - pi / 2)); % Find closest match
theta_required = theta_incidence(idx); % Required angle in degrees

% Display result
fprintf('Critical Angle: %.2f degrees\n', theta_critical);
fprintf('Required Angle of Incidence: %.2f degrees\n', theta_required);