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+//Example 2.1 // NA ,angles and pulse broadning
+clc;
+clear;
+close;
+format('v',9 )
+disp("part (a)")
+n1=1.5;//core refrative index
+n2=1.48;//claddin refractive index
+a=100/2;//radius in micro meter
+na=1;//air refrative index
+NA=sqrt(n1^2-n2^2);//numerical aperture
+disp(NA,"numerical aperture is")
+disp("part (b)")
+am=(asind(NA));//
+tm=asind(NA/n1);//
+tc=asind(n2/n1);//
+disp(am,"angle in degree is (αm)")
+disp(tm,"angle in degree is (Om)")
+disp(tc,"angle in degree is(Φc)")
+disp("part (c)")
+c=3*10^8;//speed of light in m/s
+dtl=((n1/n2)*(n1-n2)/c);//pulse broadning per unit length
+disp(dtl,"pulse broadning per unit length in sm^-1")