based on the information given redraw the diagram as follows:

Given that θ1 = 47° and θ2 = 79.5° .

Snell’s law at the first surface gives

**n sinα = 1.00 sin 47.0° **Equation 1

Also using the geometry, you can conclude that the angle of incidence of the second surface is:

**β = 90.0°− α**

Thus using snell's law we get:

**n sinβ = n sina90.0°−α f = 1.00 sin79.5° **

and so simplying we get:

**n cosα = sin79.5°** Equation 2

We can find **α**, by dividing equation 1 by equation 2:

** tanα = sin θ1 /θ2**

**α = inverse tan (****sin θ1 /θ2)**

and so we can plug α back in to equation 1 to solve for n.

Part B:

From the sketch, observe that the distance the light travels in the plastic is

**d = L / sinα**

and teh speed of light in the plastic is:

**v = c / n**

So the time required to travel through the plastic is:

**Δt = d / v**