The brilliant colours seen in a thin soap film illuminated by white light are mainly a consequence of which combination of optical phenomena?

Introduction / Context:
Thin films such as soap bubbles or oil on water often display striking coloured patterns when illuminated with white light. These colours are not due to pigments but arise from wave effects of light interacting with thin layers. This question tests whether you understand which optical phenomena are primarily responsible for such colours, an important example in the study of interference and thin film optics.

Given Data / Assumptions:

• A thin soap film of varying thickness is illuminated by white light.
• Brilliant colour bands appear when viewed from certain angles.
• The film has two surfaces: the outer and inner boundaries of the soap layer.
• The options mention polarization, diffraction, dispersion, multiple refraction and multiple reflection with interference.

Concept / Approach:
The key to understanding colours in a thin soap film is interference of light waves reflected from the two surfaces of the film. When white light strikes the film, part of the light is reflected from the top surface, and part is transmitted into the film, reflected at the lower surface, and then emerges back. These two reflected waves travel different optical path lengths. Depending on the film thickness and wavelength, they can interfere constructively or destructively, enhancing some colours while suppressing others. Because the film can be extremely thin, multiple reflections within the film also occur, but the essential phenomena are multiple reflection and interference, not dispersion or polarization.

Step-by-Step Solution:
Step 1: When white light falls on the soap film, it partially reflects from the front surface.Step 2: Some light enters the film, reflects off the back surface, and emerges again, producing a second reflected beam.Step 3: These two reflected beams have travelled paths of different lengths and may be out of phase.Step 4: For certain wavelengths and film thicknesses, constructive interference occurs, enhancing those colours; for others, destructive interference reduces intensity.Step 5: Because the film thickness changes across the surface, different colours appear at different positions.Step 6: All this arises from multiple reflections at the film interfaces combined with interference of the reflected waves.

Verification / Alternative check:
Thin film interference is a standard topic covered in optics textbooks, where soap films and oil films are used as classic examples. The explanations always involve multiple reflection and interference, sometimes with a discussion of phase changes upon reflection. Dispersion (wavelength dependent refraction) does contribute to spreading of colours in prisms, but is not the primary cause for the coloured fringes in a uniform thin film under normal incidence.

Why Other Options Are Wrong:
Polarization is about the orientation of the electric field vector and is not mainly responsible for the coloured patterns in soap films. Diffraction deals with bending of light around edges and through apertures, which is not the dominant effect here. Dispersion is the separation of colours due to different refractive indices, most notably in prisms, but it does not produce the thin banded patterns seen in soap films by itself. Multiple refraction and dispersion alone do not capture the critical role of interference between multiple reflected beams.

Common Pitfalls:
Students often confuse dispersion-based colour formation (like rainbows or prisms) with interference-based colours in thin films. Another pitfall is to assume that any colourful phenomenon must involve dispersion. To avoid confusion, remember that thin film colours depend sensitively on thickness and viewing angle, and they disappear or change when the film thickness changes, which is characteristic of interference phenomena.

Final Answer:
The brilliant colours in a thin soap film arise mainly from multiple reflection and interference of light.