Refractive index

The light passes through the interface between air and glass with a refractive index of 1.5. Find:
(a) the angle of refraction if light strikes the interface from the air at an angle of 40°.
(b) the angle of refraction when light strikes the glass interface at an angle of 40°.
(c) the angle of incidence if the light is refracted at an angle of 20° on impact from the glass.
(d) cut-off angle (justify for which way the light passes through the interface)

Correct answer:

A =  25.374 °
B =  74.6186 °
C =  30.8659 °
D =  41.8103 °

Step-by-step explanation:

n=1.5 α=40   sinα:sinA=n  A1=arcsin(sinα°/n)=arcsin(sin40° /n)=arcsin(sin40° /1.5)=arcsin(0.642788/1.5)=0.44286 A=A1  =A1 π180   =0.4429 π180   =25.374  =25.374=25°2226"
β=40   sinB:sinβ=n  B1=arcsin(n sinβ°)=arcsin(n sin40° )=arcsin(1.5 sin40° )=arcsin(1.5 0.642788)=1.30234 B=B1  =B1 π180   =1.3023 π180   =74.619  =74.6186=74°377"
γ=20   sinC:sinγ=n  C1=arcsin(n sinγ°)=arcsin(n sin20° )=arcsin(1.5 sin20° )=arcsin(1.5 0.34202)=0.53871 C=C1  =C1 π180   =0.5387 π180   =30.866  =30.8659=30°5157"
δ=90   sinδ:sinD=n  D1=arcsin(sinδ°/n)=arcsin(sin90° /n)=arcsin(sin90° /1.5)=arcsin(1/1.5)=0.72973 D=D1  =D1 π180   =0.7297 π180   =41.81  =41.8103=41°4837"

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