You may
have noticed that many good camera and projector lenses appear bluish or purplish; this is due
to a coating designed to prevent unwanted reflections from the lens surface. The surface of the
glass is coated with a material which is transparent and has a refractive index between those of
air and glass; magnesium fluoride, MgF2, with a refractive index of 1.38, is often
used.
The thickness (t) of the film is chosen to give destructive interference between
the beam reflected from the surface of the coating and that reflected from the surface of the lens
(Figure 1).
This is given by 2nt = λ/2 for
normal incidence or 2nt cos r = λ/2 for light that does not meet the
surface at right angles; a value of t of around 10-5 cm is typical.
The
value of the wavelength chosen is around 530 nm, because this is the wavelength to which the
eye is most sensitive. Removing light of this wavelength from the spectrum leaves mainly blue
and red, thus giving the characteristic purplish colour.
It can be shown that the two
reflected waves from the coating and the glass have the same intensity if the refractive index of
the coating is equal to the square root of the refractive index of the glass. If the refractive index
of the coating is greater than that of the glass then the reflection is
increased!