How Do You Calculate the Index of Refraction in a Light Refraction Problem?

[floridianfisher]

Homework Statement

A light ray enters a rectangular block of plastic at an angle 1 = 44.0° and emerges at an angle 2 = 79.0°, as shown in Figure P22.61.

Figure P22.61
(a) Determine the index of refraction of the plastic.
wrong check mark
(b) If the light ray enters the plastic at a point L = 50.0 cm from the bottom edge, how long does it take the light ray to travel through the plastic?
ns

Homework Equations

n1sin(1)=n2sin(2) or sin(critical)=n2/n1

The Attempt at a Solution

i attempted arcsin(11/44) and arcsine(79/44) but both were wrong. Can someone please help me get on the right path?

 

[Doc Al]

Treat this as two refractions and apply Snell's law at each interface. Hint: How does the second angle (the angle of refraction) at the first interface relate to the first angle (angle of incidence) at the second interface?

 

[floridianfisher]

I have sin(44)=nsin(theta2) and sin(79)=nsin(theta2) but that cannot be correct. I know that the angle of incidence and angle of refraction are equal. Please help I am mising something here.
Thanks

 

[Doc Al]

I have sin(44)=nsin(theta2) and sin(79)=nsin(theta2) but that cannot be correct.

True, that cannot be correct, since $\sin 44 \neq \sin 79$.

I know that the angle of incidence and angle of refraction are equal.

They are related, but not equal.

For clarity, I'll rewrite the equations as:
$$\sin 44 = n \sin \theta_a$$
$$\sin 79 = n \sin \theta_b$$

Find the simple trignometric relationship between $\theta_a$ & $\theta_b$ by examining the diagram. Look for triangles.