| Date | May 2013 | Marks available | 3 | Reference code | 13M.3.HL.TZ1.13 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Determine | Question number | 13 | Adapted from | N/A |
Question
This question is about thin-film interference.
The anti-reflective coating of a lens consists of a thin layer of a suitable material placed between the air and the glass of the lens.
The following data are available.
Refractive index of air = 1.0
Refractive index of coating = 1.2
Refractive index of glass = 1.5
State what phase change occurs on reflection at the air-coating boundary and at the coating-glass boundary.
The thickness d of the coating layer is 110 nm.
Determine the wavelength for which there is no resultant reflection from the surface of the lens for light at normal incidence (θ = 0º ).
Markscheme
180º / π;
path difference must be \(\frac{\lambda }{2}\);
physical thickness must be \(\frac{\lambda }{2n}\);
so, maximum wavelength \(\left( {{\rm{is}}\left[ {2nt = \left[ {m + \frac{1}{2}} \right]\lambda } \right] \to \lambda = 4{n_c}d} \right) = 528\left( {{\rm{nm}}} \right)\);
Allow any valid alternative method.
Examiners report
was well done in general
Was poorly understood. There were some good answers but many candidates omitted n or put n = 1 as in a diffraction grating.
