A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45. Determine the minimum thickness for the film if it is to be non-reflecti

The minimum thickness for the film can be determined using the equation: t = (m + 1/2) * ?0 / (2 * n * cos?) where t is the thickness of the film, m is an integer, ?0 is the wavelength of the incident light in vacuum (560 nm in this case), n is the refractive index of the lens (1.61 in this case), and ? is the angle of incidence (assumed to be zero here). To avoid reflection, the phase shift upon reflection at both interfaces (lens-film and film-air) should be equal and opposite. This can be achieved by choosing the thickness of the film such that it is equal to an odd multiple of {eq}frac{lambda_0}{4n_{film}} {/eq} where {eq}n_{film} {/eq} is the refractive index of the film. Substituting the given values in the equation and solving for the thickness, we get: t = (m + 1/2) * ?0 / (4 * n_{film} * cos?) n_{film} = 1.45 (given) ? = 0 degrees (assumed) For minimum thickness (m = 0), we get: t = ?0 / (8 * n_{film}) = (560 nm) / (8 * 1.45) = 48.28 nm Therefore, the minimum thickness for the film to be non-reflecting for the given wavelength is 48.28 nm.