Final answer:
The thinnest film of MgF2 on glass that produces a strong reflection for light with a wavelength of 490 nm is approximately 177 nm.
Step-by-step explanation:
The thinnest film of MgF2 (n = 1.39) on glass that produces a strong reflection for light with a wavelength of 490 nm can be calculated using the formula for destructive interference in a thin film:
2t = (m + 1/2) * λ / n
In this formula, t is the thickness of the film, λ is the wavelength of light, n is the refractive index of MgF2, and m is an integer representing the order of the destructive interference.
Since we want to find the thinnest film that produces a strong reflection, we assume m = 0. Plugging in the given values, we have:
2t = (0 + 1/2) * 490 nm / 1.39
Solving for t, we find that the thinnest film is approximately 177 nm.