Calculate the refractive index of the material for the glass prism in the diagram above

Answer Details

To calculate the refractive index of the material for the glass prism in the diagram, we need to use Snell's law. Snell's law 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 refractive indices of the two media.
In this case, we can assume that the light is traveling from air into the glass prism. Let's call the angle of incidence θ1 and the angle of refraction θ2. We know that θ1 = 45°, and we can measure θ2 from the diagram.
Now we can use Snell's law:
sin(θ1)/sin(θ2) = n1/n2
where n1 is the refractive index of air, which is approximately 1, and n2 is the refractive index of the glass prism, which we want to find.
Rearranging the equation, we get:
n2 = n1*sin(θ1)/sin(θ2)
Plugging in the values we know, we get:
n2 = 1*sin(45°)/sin(θ2)
We can use trigonometry to find sin(θ2) based on the values in the diagram:
sin(θ2) = (1/2)*sin(90°-θ2) = (1/2)*sin(θ1) = (1/2)*(√2/2) = √2/4
Plugging this back into the equation, we get:
n2 = 1*sin(45°)/(√2/4) = 2/√2 = √2
Therefore, the refractive index of the material for the glass prism is √2.