Which of the following conditions are necessary and sufficient for total internal reflection to take place at…

Analysis of the Question

Total internal reflection (TIR) is a phenomenon in optics that occurs when light traveling through a medium hits a boundary with a less dense medium at a specific angle. To identify the correct conditions, we must look at the physical requirements for this phenomenon to occur.

Concept Explanation

Total internal reflection occurs only when two specific conditions are met:

1. Direction of Light: Light must travel from a medium with a higher refractive index (optically denser) to a medium with a lower refractive index (optically less dense). If light travels from a less dense to a denser medium, it bends towards the normal, making it impossible for the light to be reflected back into the first medium.
2. Angle of Incidence: The angle of incidence must be greater than the critical angle ($c$). The critical angle is the angle of incidence for which the angle of refraction is exactly $90^\circ$. If the angle of incidence is less than the critical angle, the light will refract (pass through) into the second medium.

Step-by-Step Solution

• Condition I: "Light is passing from optically denser medium to optically less dense medium." This is a necessary condition for TIR.
• Condition II: "Light is passing from optically less dense medium to optically denser medium." This is incorrect because light would bend towards the normal, not reflect.
• Condition III: "Angle of incidence is greater than a certain critical value." This is a sufficient condition. Once the light is in the denser medium, exceeding the critical angle ensures the light reflects back.
• Condition IV: "Angle of incidence is lesser than a certain critical value." This is incorrect because, at angles less than the critical angle, refraction occurs instead of total internal reflection.

Comparing these to the options provided, conditions I and III are the correct requirements.

Conclusion

Exam Tip

Remember the acronym "D-G" for Total Internal Reflection:

• Denser to rarer medium.
• Greater than the critical angle. If you remember "D-G," you will never miss a question on the conditions for TIR!