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

Explanation

The light of wavelength `lambda` is strongly reflected if
`2mud =(n + (1)/(2)lambda …. (i)`
Where n is a nonnegative integer.
Here, `2mud = 2xx 1.50 xx 0.5 xx 10^(-6)m`
`=1.5 xx 10^(-6)m…. (ii)`
Putting `lambda = 400 nm` in (i) and using (ii),
`1.5 xx 10^(-6)m = (n + (1)/(2)) (400xx10^(-9) m)`
or , n = 3.25.
Putting `lambda = 700 nm` in (ii),
`1.5xx10^(-6) m = (n +(1)/(2)) (700 xx 10^(-9)m)`
or, n= 1.66.
Thus, between 400 nm and 700 nm the integer n can take the values 2 and 3. Putting these values of n in (i), the wavelength become
`lambda= (4mud)/(2n + 1) = 600 nm and 429 nm.`
Thus, light of wavelengths 429nm and 600 nm are strongly reflected.