A glass plate (n=1.53) that is 0.485 ` mu` m thick and surrounded by air is illuminated by a beam of white light normal to the plate.
(a) What wavelengths (in air) within the limits of the visible spectrum `(lambda = 400 "to" 700 nm)` are intensified in the reflected beam ?
(b) What wavelengths within the visible spectrum are intensified in the transmitted light?

Explanation

(a) Ray-1 is reflected from a denser medium and ray-2 by a raster medium.

`Delta x = 2nt = (2m-1)lambda/2` for maximum intensity
`:. lambda= (4nt)/(2m-1)`
` = ((4)(1.53)(485nm))/(2m-1)`
` = (2968/(2m-1))`nm
For `m=1, lambda=2968nm`
For `m=2, lambda= 989nm `
` For `m=3, lambda= 594nm`
For `n=4, lambda=424nm`
For `n=5, lambda= 329nm `
Therefore, two wavelengths lying in the given
range are `424nm` and `594nm`.
(b) Ray -1 and ray-2 are in same phase.

Hence,
`Deltax = 2nt = mlambda (for maximum intensity)`
`:. lambda = (2nt)/m = ((2)(1.53)(485 nm))/m`
=(1484/m) nm
Substituting m= 1,2,3....... etc.
`lambda_1 = 1484 nm lambda_2= 742 nm, `
`lambda_3 = 495 nm , lambda_4 = 371 nm etc.`
Therefore, only wavelength lying in the given range is 495 nm.