Final answer:
The thickness of the thin film placed on a flat glass surface, with a refractive index of 1.50, can be calculated using the formula t = Δx / (2n), where t is the thickness, Δx is the path difference, and n is the refractive index. By plugging in the values, we find that the thickness is 166.7 nm. Therefore, the correct option is d).
Step-by-step explanation:
In this problem, we have a thin film with an index of refraction of n = 1.50 placed on a flat glass surface. When a thin film is surrounded by a medium with a higher index of refraction, the reflected light undergoes a phase change of π radians. This means that for destructive interference, the path difference between the reflected rays must be equal to half a wavelength.
Using the formula for the path difference in a thin film, which is given by Δx = 2nt, where Δx is the path difference, n is the refractive index of the film, and t is the thickness of the film, we can rearrange the formula to solve for the thickness:t = Δx / (2n). Plugging in the values, we have t = (500 nm) / (2(1.50)) = 166.7 nm. Therefore, the correct answer is 166.7 nm (option d).