answer: the correct answer id option(d).
explanation:
snell's law refraction:
![\frac{n_2}{n_1}=\frac{sin \theta_1}{sin\theta_2}](/tex.php?f=\frac{n_2}{n_1}=\frac{sin \theta_1}{sin\theta_2})
the angle of refraction = ![\theta_2=38 ^o](/tex.php?f=\theta_2=38 ^o)
the angle of incidence =![\theta_1=?](/tex.php?f=\theta_1=? )
refractive index of air =
= 1
refractive index of glycerol
= 1.47
![\frac{1.47}{1}=\frac{sin\theta_1}{sin 38^o}, (sin38^o=0.61)](/tex.php?f=\frac{1.47}{1}=\frac{sin\theta_1}{sin 38^o}, (sin38^o=0.61))
![sin\theta_2=0.8967](/tex.php?f=sin\theta_2=0.8967)
![\theta_2=24.2^o, (sin^{-1}0.8967=63.72^o)](/tex.php?f=\theta_2=24.2^o, (sin^{-1}0.8967=63.72^o))
from the given options, the most closest answer to 63.72° is 65° of option (d).