Final answer:
In a Newton's rings pattern, the rings become narrower as you move outward from the centre because the film thickness changes more rapidly with increasing distance from the centre. This effect is related to thin-film interference in the gap between two lenses.
Step-by-step explanation:
The correct way to complete the following statement: 'In a Newton's rings interference pattern the rings become narrower as you move outward from the centre because the film thickness changes more rapidly with increasing distance from the centre.' This is an observation attributed to the optical phenomenon known as thin-film interference. In the context of Newton's rings, when two lenses are placed together, the air film between them varies in thickness from the point of contact (center) towards the edges. As a result, the interference condition changes with distance from the center, with each ring representing a constant change in film thickness, corresponding to half a wavelength shift in the light path.