I'm not getting the correct result for the u, i want it in degree but the ans is not right, the plot is not smooth.

ni = 1;

nt = 1.5;

t = 0:0.1:1.57;

oi = rad2deg(t);

u = asind((nt.*sin(oi))./ni);

ot = abs(u);

r1 = -(sind(oi-ot)./sind(oi+ot));

plot(oi,r1);

Answer 1

[Davide Masiello]

You did not give enough information to know what the end result should be, but if your interest is only to plot in degrees, then I would perform all the calculations in radians in order to avoid confusion and convert into degrees only in the plot. See below for example

ni = 1;
nt = 1.5;
t = 0:0.001:pi/2;
u = asin(nt*sin(t)/ni);
r1 = -(sin(t-abs(u))./sin(t+abs(u)));
plot(rad2deg(t),r1);
xlabel('t, $^{\circ}$','Interpreter','latex')
ylabel('$r_1$','Interpreter','latex')

Answer 2

[Sam Chak]

To understand why it is not smooth, you need to see what causes the singularity (division-by-zero) at around .

ni = 1;
nt = 1.5;
% t  = 0:0.1:1.57;
% oi = rad2deg(t);
oi = linspace(0, 90, 9001);
u  = asind(nt*sind(oi)/ni);     % <-- correction to your trigonometric function
ot = abs(u);
r1 = - (sind(oi - ot)./sind(oi + ot));
plot(oi, r1); ylim([-15 15]), grid on, xlabel('o_{i} (deg)'), ylabel('r_{1}')

subplot(211)
plot(oi, sind(oi - ot)), title('sind(oi - ot)'), grid on, xlabel('o_{i} (deg)')
subplot(212)
plot(oi, sind(oi + ot)), title('sind(oi + ot)'), grid on, xlabel('o_{i} (deg)')

ans = 75.7100

Answer 3

[Walter Roberson]

oi = rad2deg(t);
u = asind((nt.*sin(oi))./ni);

You convert to degrees but then sin() which is a radian operation. You used the correct sind() in later lines.