To understand why the correct answer is option 'B', let's break down the problem step by step.

Given:
- The wave is a transverse electromagnetic (TEM) wave, which means it has both electric and magnetic field components perpendicular to the direction of propagation.
- The dielectric boundary has a refractive index of r1 = 4 on one side and r2 = 3 on the other side.
- We need to find the angle of incidence for total reflection.

1. Understanding the Refractive Index:
The refractive index (r) is a measure of how light propagates through a medium. It is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). Mathematically, r = c/v.

2. Snell's Law:
Snell's law relates the incident angle (θ1), the refracted angle (θ2), and the refractive indices of the two media. It states that r1 * sin(θ1) = r2 * sin(θ2).

3. Total Internal Reflection:
When the angle of incidence is greater than the critical angle, total internal reflection occurs. The critical angle (θc) is the angle of incidence that results in an angle of refraction of 90 degrees. It can be calculated using the formula sin(θc) = r2 / r1.

4. Calculating the Critical Angle:
In this case, r1 = 4 and r2 = 3. Substituting these values into the formula, we get sin(θc) = 3/4. Taking the inverse sine of both sides, we find θc ≈ 48.59 degrees.

5. Finding the Angle of Incidence for Total Reflection:
Since we are looking for the angle of incidence for total reflection, we need to find the angle at which total internal reflection occurs. By symmetry, the angle of incidence for total reflection is equal to the critical angle, which is approximately 48.59 degrees.

Therefore, the correct answer is option 'B' (60 degrees).

Overall, it's important to understand the concepts of refractive index, Snell's law, and total internal reflection to solve this problem.