To solve this problem it is necessary to apply Snell's law and thus be able to calculate the angle of refraction.
From Snell's law we know that
[tex]n_1sin\theta_1 = n_2 sin\theta_2[/tex]
Where,
n_i = Refractive indices of each material
[tex]\theta_1[/tex] = Angle of incidence
[tex]\theta_2[/tex] = Refraction angle
Our values are given as,
[tex]\theta_1 = 38\°[/tex]
[tex]n_1 = 1[/tex]
[tex]n_2 = 1.4[/tex]
Replacing
[tex]1*sin38 = 1.4*sin\theta_2[/tex]
Re-arrange to find [tex]\theta_2[/tex]
[tex]\theta_2 = sin^{-1} \frac{sin38}{1.4}[/tex]
[tex]\theta_2 = 26.088°[/tex]
Therefore the angle will the beam make with the normal in the glass is 26°
