5. A beam of light travels from benzene to water. If the angle of incidence in the benzene is 48, what will be the angle of refraction in the water?
To determine the angle of refraction, you can use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.
Mathematically, Snell's Law can be written as:
sin(θ1) / sin(θ2) = v1 / v2
where θ1 is the angle of incidence, θ2 is the angle of refraction, v1 is the speed of light in the first medium (benzene), and v2 is the speed of light in the second medium (water).
Given that the angle of incidence (θ1) in benzene is 48 degrees, we need to find the angle of refraction (θ2) in water.
Assuming the speed of light in a vacuum is approximately equal to the speed of light in benzene, we can use the refractive index to calculate the speed of light in water.
The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. The refractive index of benzene is typically around 1.501, and the refractive index of water is about 1.333.
Using the equation:
n = c / v
where n is the refractive index, c is the speed of light in a vacuum, and v is the speed of light in the medium, we can solve for v2:
v2 = c / n2
Since the speed of light in a vacuum is about 3 × 10^8 meters per second, we can calculate v2:
v2 = (3 × 10^8 m/s) / 1.333
Now that we know the speed of light in water (v2), we can use Snell's Law to find the angle of refraction (θ2):
sin(θ1) / sin(θ2) = v1 / v2
Rearranging the formula to solve for θ2:
sin(θ2) = (sin(θ1) * v2) / v1
Finally, we can substitute the given values and calculate the angle of refraction (θ2) in water.