add lab1

lab1/refraction.m

+# Code gives error if no solution in [0,pi/2] exits for given nx,ny.
+
+function y = refraction(i)	#defining the function whose roots are to be found
+a = load('input_inlab_task_A1.txt');	#taking input from file
+nx = a(1);
+ny = a(2);
+y = sin(i) - (nx*cos(i) + ny*sin(i))*sin(i/3);	#function
+endfunction
+left =0.0001;
+
+#find left,right by iteration
+if refraction(pi/2) >0
+	for n=[0.0001:0.001:pi/2]
+	if refraction(n)<0 
+		left = n;
+		break;
+	end
+	end
+end
+if refraction(pi/2) <0
+	for n=[0.0001:0.001:pi/2]
+	if refraction(n)>0 
+		left = n;
+		break;
+	end
+	end
+end
+
+right = pi/2+0.00001;	#defined range for i solution
+x0 = [left right];
+[i,info] = fzero("refraction", x0);	#solving the function in given range
+fid = fopen ("output_inlab_task_01.txt", "w");	#writing to text file
+fdisp (fid,i);
+fclose (fid);