A beam of light is incident on a thin glass plate (refractive index 1.8). If the angle of incidence of the beam of light is 50 degrees, with what angle does the light leave the other side of the glass plate? Put your answer in degrees and don't give units.

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 refraction is equivalent to the ratio of velocities of light in the two media, or equivalently, to the opposite ratio of the indices of refraction.

The formula for Snell's law is:

n1 * sin(θ1) = n2 * sin(θ2)

Where:

• n1 and n2 are the refractive indices of the first and second medium respectively,
• θ1 is the angle of incidence,
• θ2 is the angle of refraction.

In this case, the light is going from air (with a refractive index of approximately 1) into glass (with a refractive index of 1.8). So, n1 is 1, n2 is 1.8, and θ1 is 50 degrees. We want to find θ2, the angle of refraction.

First, we need to convert the angle of incidence from degrees to radians because the trigonometric functions in most programming languages use radians, not degrees.

θ1 = 50 degrees = 50 * π/180 radians = 0.87266 radians.

Then, we can rearrange Snell's law to solve for θ2:

sin(θ2) = (n1/n2) * sin(θ1)

Substituting the known values:

sin(θ2) = (1/1.8) * sin(0.87266)

Calculating the right side gives:

sin(θ2) = 0.47942

To find θ2, we take the arcsine (inverse sine) of 0.47942:

θ2 = arcsin(0.47942) = 0.50068 radians

Finally, we convert θ2 from radians back to degrees:

θ2 = 0.50068 * 180/π = 28.68 degrees

So, the light leaves the other side of the glass plate at an angle of approximately 28.68 degrees.