Final answer:
To find the index of refraction (n) of the medium where total internal reflection occurs at an angle of 50°, we use the formula for critical angle. The calculation shows that n must be less than 1.0724 but since it cannot be less than 1 (the index of refraction of air), n is approximately 1.
Step-by-step explanation:
The concept being discussed in this question is total internal reflection, which occurs when a light ray traveling from a medium with a higher index of refraction to a medium with a lower index of refraction strikes the boundary at an angle greater than the critical angle. The index of refraction for the original medium (n1) is given as 1.4. At an angle of 50° with respect to the normal, the ray experiences total internal reflection. To find the index of refraction (n) of the new medium, we use Snell's law of refraction and the concept of critical angle.
The critical angle (θc) can be calculated using the formula for critical angle: sin(θc) = n/n1, where n is the index of refraction of the second medium, and n1 is the index of refraction of the first medium. Since the angle of incidence for total internal reflection is equal to the critical angle and the angle of refraction is 90°, we rearrange the formula to solve for n: n = n1 * sin(θc).
Given that n1 = 1.4 and θc = 50°, we plug these values into the formula: n = 1.4 * sin(50°).
we find that sin(50°) ≈ 0.7660,
hence n≈ 1.4 * 0.7660
≈ 1.0724.
Since total internal reflection occurs, n must be less than 1.0724 for the given conditions.
However, n cannot be less than 1 (the index of refraction for air), so we can conclude that n is approximately 1.