A slab of glass has a 0.800 cm thick layer of water on top of it. A light ray strikes the water at an incident angle of 64.0°. At what angle does the light ray travel through the glass?

To solve this problem, we need to use Snell's Law, which states that the ratio of the sine of the angles of incidence and transmission is equivalent to the ratio of the indices of refraction. The formula is:

n1 * sin(θ1) = n2 * sin(θ2)

Where: n1 and θ1 are the refractive index and angle of incidence in the first medium (water in this case) n2 and θ2 are the refractive index and angle of transmission in the second medium (glass in this case)

The refractive index of water is approximately 1.33 and that of glass is approximately 1.52.

First, we need to find the angle of transmission in the water. We rearrange Snell's Law to solve for θ2:

θ2 = arcsin[(n1 * sin(θ1)) / n2]

Substituting the given values:

θ2 = arcsin[(1.33 * sin(64.0°)) / 1.52]

Calculate the above expression to find the angle of transmission in the water.

Next, we use Snell's Law again to find the angle of transmission in the glass. This time, n1 and θ1 are the refractive index and angle of transmission in the water, and n2 is the refractive index of the glass.

θ2 = arcsin[(n1 * sin(θ1)) / n2]

Substitute the values:

θ2 = arcsin[(1.33 * sin(θ2 from previous calculation)) / 1.52]

Calculate the above expression to find the angle of transmission in the glass. This is the angle at which the light ray travels through the glass.