Question

White light is incident normally on a glass plate of thickness `0.50 xx 10^(-6)` and index of refraction 1.50. Which wavelengths in the visible region `(400 nm - 700 nm)` are strongly reflected by the plate?

Answer 1

The light of wavelength `lambda` is strongly reflected if
`2 mu d = (n + (1)/(2)) lambda`
Where n is a non-negative integer.
Here `2 mu d = 2 xx 1.50 xx 0.5 xx 10^-6 m = 1.5 xx 10^-6 m`.
Putting `lambda = 400` nm in Eq.(i), we get
`1.5 xx 10^-6 m = (n + (1)/(2)) (400 xx 10^-(6) m)`
or ` n = 3.25`
Putting `lambda = 700 nm` in Eq. (i), we get
`1.5 xx 10^(-6) m = (n + (1)/(2)) (700 xx 10^(-9) m)`
or `n = 1.66`
Thus, within 400 nm to 700 nm, the integer n can take the values 2 and 3. Putting these values of n in (i), the wavelengths become
` lambda = (4 mu d)/(2 n + 1) = 600 nm and 429 nm`
Thus, light of wavelenghts 429 nm and 600 nm are strongly reflected.