A ray of light is incident at an angle of 20degrees to the normal on one face of an equilateral prismm made in glass of refractive index 1.523. Trace the ray of light through the prism and find the total deviation produced.
Do i find i1' first?
sini1'= n1/n1'sini1
i1'= 1/1.523sin20
i1'=13degrees?
To trace the ray of light through the prism and find the total deviation produced, we need to use Snell's law and the concept of total internal reflection.
Here's how you can do it step by step:
1. Draw an equilateral triangle to represent the prism. Label the vertices as A, B, and C.
2. Draw a line perpendicular to the base of the triangle at point B. This represents the normal at the point of incidence.
3. Draw a line representing the incident ray, making an angle of 20 degrees with the normal (line from point A).
4. Apply Snell's law at the first surface of the prism. Snell's law states that n1 * sinθ1 = n2 * sinθ2, where n1 is the refractive index of the medium from which the light is coming, θ1 is the angle of incidence, n2 is the refractive index of the medium in which light is entering, and θ2 is the angle of refraction.
In this case, the incident medium is air with a refractive index of approximately 1 (considered negligible), and the refractive index of the glass prism is given as 1.523. Therefore, the equation becomes:
1 * sin(20°) = 1.523 * sin(θ2)
Solve for θ2. The value of θ2 will be the angle at which the ray enters the prism after refraction.
5. Extend the refracted ray inside the prism until it hits the opposite surface (line from point A extended).
6. Apply Snell's law again at this interface between the prism and air (or air and prism). The equation will now be:
1.523 * sin(θ2) = 1 * sin(θ3)
Solve for θ3. The value of θ3 will be the angle at which the ray exits the prism after refraction.
7. If θ3 > 90 degrees, total internal reflection occurs, and the ray reflects back into the prism. In this case, draw the reflected ray extending from the point of total internal reflection (line perpendicular to the base of the triangle at point D and then extending backward).
8. Calculate the angle of incidence during total internal reflection using the equation: sin(θ4) = 1.523 * sin(90°)
Solve for θ4. The value of θ4 will be the angle at which the ray reflects backward after total internal reflection.
9. Calculate the total deviation produced. The total deviation is the sum of the angles θ2, θ3, and θ4. Add the values of these angles to find the total deviation.
Total deviation = θ2 + θ3 + θ4
That's it! By following these steps, you can trace the ray of light through the prism and find the total deviation produced.