In geometrical optics, during total internal reflection, light travels from which type of medium to which other type, and what happens to its intensity in the ideal case?

Introduction / Context:
Total internal reflection is a striking optical phenomenon that explains how light can be trapped inside glass fibres, raindrops and gemstones. It occurs when a light ray tries to pass from a medium with higher refractive index to a medium with lower refractive index at an angle of incidence greater than a certain critical angle. Instead of refracting into the second medium, the light is completely reflected back into the first medium. This question asks from which type of medium to which other type light must travel for total internal reflection to occur, and what happens to the intensity of the reflected light in the ideal case.

Given Data / Assumptions:
• We are dealing with the interface between two transparent media. • One medium is optically denser (higher refractive index) and the other is optically rarer (lower refractive index). • The angle of incidence in the denser medium exceeds the critical angle. • Idealised conditions ignore absorption and scattering losses.

Concept / Approach:
Total internal reflection has two necessary conditions. First, light must travel from an optically denser medium to an optically rarer medium, for example from glass to air or from water to air. Second, the angle of incidence in the denser medium must be greater than the critical angle, which is defined as the angle of incidence for which the angle of refraction in the rarer medium becomes 90 degrees. Under these conditions, Snell law indicates that no refracted ray exists and all of the incident energy is reflected back into the denser medium. In the ideal limit, the reflection is total and there is no loss of intensity on reflection, unlike ordinary reflection where some energy is transmitted or absorbed.

Step-by-Step Solution:
Step 1: Identify that total internal reflection can happen only when the light tries to go from a medium of higher refractive index to one of lower refractive index. Step 2: Recognise that this means light must travel from a denser medium to a rarer medium, such as glass to air or water to air. Step 3: Recall that at the critical angle, the refracted ray would travel along the interface. Step 4: Note that for angles of incidence greater than the critical angle, Snell law has no real refraction solution, and instead the wave is completely reflected back into the denser medium. Step 5: Understand that in the ideal case, all of the incident light energy is reflected, so the intensity of the reflected ray equals the intensity of the incident ray. Step 6: Conclude that the correct description is denser to rarer medium with no loss of intensity in the idealised situation.

Verification / Alternative check:
Practical examples support this description. Optical fibres rely on total internal reflection of light inside a core with higher refractive index surrounded by cladding of lower refractive index; light is guided along the fibre with very low loss over long distances. Similarly, sparkling effects in diamonds arise because light is trapped by repeated total internal reflections inside the denser diamond and only escapes after multiple reflections. In theoretical treatments, reflectivity at angles above the critical angle is taken as 100 percent for ideal, non absorbing media. These examples confirm that the direction is from denser to rarer and that intensity is preserved in the ideal case.

Why Other Options Are Wrong:
Option A and option C describe light travelling from a rarer to a denser medium, which is the ordinary refraction scenario where total internal reflection cannot occur. In such cases, light bends toward the normal and part of it may be reflected, but not totally. Option C and option D mention loss of intensity, which applies to partial reflection and transmission, not to ideal total internal reflection where reflectivity is unity. Real materials do have slight absorption, but the phenomenon is defined in terms of complete reflection of the wave. Therefore, only the option describing travel from denser to rarer medium with no loss of intensity matches the textbook definition.

Common Pitfalls:
A common confusion is to think of total internal reflection as just a stronger version of normal reflection at any interface, regardless of direction. Students may forget that the direction from optically denser to optically rarer medium is essential. Another pitfall is to assume that some fractional transmission must always occur; in the special case of total internal reflection, the transmitted wave is replaced by an evanescent field that does not carry energy far into the rarer medium. Remembering the two conditions denser to rarer and angle greater than critical makes it easier to identify when total internal reflection can happen and how it behaves.

Final Answer:
The correct choice is From a denser to a rarer medium and it occurs with no loss of intensity, because total internal reflection only occurs for light travelling from higher to lower refractive index at angles greater than the critical angle, and in the ideal case all the incident light energy is reflected back into the denser medium.