madam, i do not know what core/ clads are but my calculation shows that between 0 and 90 degrees, alpha has to be less than 17degrees .( on both sides, ie. a cone of 17 degree semi vertical angle)
if this matches answers, then i will tell u to just draw the figure neatly, apply snell law at two surfaces, one at air -core interface when ray enters core and the other at core - clad interface and apply total internal reflection conditions.if u need further explanation, please reply.
the relevant equations are 1 sin(alpha)=1.46 sin theta eq1 ......snell law at core air interface
so angle of incidence at core clad interface=90 - theta
critical angle = sin inverse(1.43/1.46)
so for TOTAL INT REFLECSION, 90 - theta>sin inverse(1.43/1.46)
so theta<90- sin inverse (1.43/1.46), take sine on both sides
sin theta<cos(sin inverse 1.43/1.46)
ie. sin theta<0.201677
now use eq 1 to replace sin theta, sin alpha/1.46<.201677
or, sin alpha<0.294448637
taking inverse
alpha< 17.1244 degrees.