The normal in the water is 29.8°
Let
[tex]n_i=[/tex] the index of refraction for the material with incident light,
[tex]n _r[/tex] = the index of refraction for the material with refracted light,
[tex]\theta_i=[/tex] the angle of incidence
[tex]\theta_r[/tex] = the angle of refraction.
Applying Snell's law
[tex]n_isin\theta_i=n_rsin\theta_r[/tex]
Given
[tex]n_a=1, n_g=1.550, n_m=1.329n[/tex]
a)
From air to glass
[tex]n_a sin\theta_1[/tex][tex]=n_gsin\theta_2[/tex]
[tex]1\\sin *41.3 = 1.550 *sin\theta_2[/tex]
A normal from glass to water
[tex]n_g sin\theta_2 =n_m sin \theta_3 \\1.550\cdot\sin25.2\degree=1.329\cdot\sin\theta_3\\1.550*sin25.2=1.329*sin\theta_3 \\\theta_3=\arcsin({1.550\cdot \sin25.2\degree \over 1.329})\\\approx29.8\theta_3 =arc sin( 1.3291*550*sin25) ≈ 29.8[/tex]
Hence the normal in the water is 29.8°
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