3. a beam of light enters water from air.(a) if its angle of incidence is 70,what is the angle of refraction ?(b) at what angle must it enter the water if its angle of refraction is to be 20?
To determine the angle of refraction when a beam of light enters water from air, we need to use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence (θ1) to the sine of the angle of refraction (θ2) is equal to the ratio of the speeds of light in the two mediums (n2/n1).
(a) Given that the angle of incidence (θ1) is 70 degrees, and the light is entering water from air, we know that the speed of light in air (n1) is approximately 1 and the refractive index of water (n2) is approximately 1.33.
We can use Snell's law to find the angle of refraction (θ2) using the equation:
sin(θ1) / sin(θ2) = n2 / n1
sin(70) / sin(θ2) = 1.33 / 1
To find the angle of refraction (θ2), rearrange the equation:
sin(θ2) = sin(70) / 1.33
θ2 = arcsin(sin(70) / 1.33)
Using a calculator, compute the arcsin to find:
θ2 ≈ 49.33 degrees
Therefore, when the angle of incidence is 70 degrees, the angle of refraction is approximately 49.33 degrees.
(b) Now, let's determine at what angle the beam of light must enter the water if the angle of refraction is to be 20 degrees.
Using Snell's law, we can rewrite the equation as:
sin(θ1) / sin(θ2) = n2 / n1
sin(θ1) / sin(20) = 1.33 / 1
To find the angle of incidence (θ1), rearrange the equation:
sin(θ1) = sin(20) / 1.33
θ1 = arcsin(sin(20) / 1.33)
Using a calculator, compute the arcsin to find:
θ1 ≈ 34.92 degrees
Therefore, the beam of light must enter the water at approximately 34.92 degrees for the angle of refraction to be 20 degrees.