Refraction Of Light

To solve this problem, we need to clearly understand the concept of the critical angle and how it relates to the refractive indices of the materials involved:

1. Understanding Critical Angle:
   • The critical angle is the angle of incidence above which total internal reflection occurs when light passes from a medium with a higher refractive index to a medium with a lower refractive index.
   • The relationship between the critical angle and refractive indices is given by Snell's Law at the critical angle: where is the refractive index of the first medium and is that of the second medium.
2. Given Problem Information:
   • Refractive indices:
3. Calculating Critical Angles:
   • First, note that and .
   • Using the given condition :
   • Since , it implies .
4. Solving for :
   • Substitute in the equation :
   • Now, using :
5. Conclusion:
   • The value of calculated does not match any provided option for . Hence, an error may have occurred in the given options or conditions.
   • Revisiting the particular options, it appears that there has been a mismatch, but the calculation of solving general condition shows that provided result cannot be correct since sine function cannot have negative values greater than -1. Correctly calculated discrete values like etc., imply an error in the presumption provided.
   • Thus, logical reasoning indicates to revise calculation or retry implementation based on textbook standards over mis-choice inconsistencies.