1.A light ray enters from air (n1 = 1.0) onto glass (n2 = 1.5). Calculate Θ2 (transmission angle) values for Θ1 (incident angle) values 10, 20, 30, 40, 50, 60, 70, 80 degrees, respectively.
I will be happy to critique your calcs.
Use Snell's Law.
sini÷sinr=nr÷ni
To calculate the transmission angle (Θ2), you can use Snell's law, which relates the incident angle (Θ1) and the transmission angle (Θ2) to the refractive indices of the two media involved.
The formula for Snell's law is:
n1 * sin(Θ1) = n2 * sin(Θ2)
Where:
- n1 is the refractive index of the incident medium (in this case, air)
- n2 is the refractive index of the transmitted medium (in this case, glass)
- Θ1 is the incident angle (the angle between the incident ray and the surface normal)
- Θ2 is the transmission angle (the angle between the transmitted ray and the surface normal)
Given: n1 = 1.0 (air) and n2 = 1.5 (glass)
Let's calculate Θ2 for the given Θ1 values:
For Θ1 = 10 degrees:
sin(Θ2) = (n1 / n2) * sin(Θ1)
sin(Θ2) = (1.0 / 1.5) * sin(10)
Θ2 = sin^(-1)((1.0 / 1.5) * sin(10))
Θ2 ≈ 6.53 degrees
Similarly, you can calculate Θ2 for the other given Θ1 values (20, 30, 40, 50, 60, 70, and 80 degrees) using the same formula.
For Θ1 = 20 degrees:
Θ2 ≈ 13.08 degrees
For Θ1 = 30 degrees:
Θ2 ≈ 19.67 degrees
For Θ1 = 40 degrees:
Θ2 ≈ 25.89 degrees
For Θ1 = 50 degrees:
Θ2 ≈ 31.81 degrees
For Θ1 = 60 degrees:
Θ2 ≈ 37.38 degrees
For Θ1 = 70 degrees:
Θ2 ≈ 42.58 degrees
For Θ1 = 80 degrees:
Θ2 ≈ 47.34 degrees
So, the Θ2 values corresponding to the given Θ1 values are approximately:
Θ2 = 6.53, 13.08, 19.67, 25.89, 31.81, 37.38, 42.58, 47.34 degrees respectively.