An object O is in front of a thick glass mirror, silvered on its back surface. The object emits blue light of wavelength λ=5.1×10−7m in air. The refractive index of the glass is n=1.4.
Assuming that half of the amplitude of the light is reflected at the air-glass interface, what is the smallest thickness of the glass for which no light returns normally from the mirror? Ignore any phase change due to reflection.
I tried this and I don't know where I went wrong
distance=speed x time
distance= 2.14x10^8 x 2.38x10^-15=5.1x10^-7 m
Find the period of the light in air.
If the light that travels within the glass is to meet this light again in antiphase, it has half of this time to do it, ie it has to travel from the air-glass boundary to the silver coating and back again in this time.
I was surprised that this gave me the correct answer right away, I was put off by the "thick glass" because my answer doesn't sound very thick at all....