Question

please answer both :)

Dispersion in a window pane. In Figure (a) below, a beam of white light is incident at angle 6, -50° on a common window pane (shown in cross section. For the pane's type of glass, the index of refraction for visible light ranges from 1.527 at the blue end of the spectrum to 1.518 at the red end. The two sides of the pane are parallel. What is the angular spread of the colors in the beam (a) when the light enters the pane and (b) when it emerges from the opposite side? (Hint: When you look at an object through a window pane, are the colors in the light from the object dispersed as shown in, say, Figure (b)?) White light (a) Number Units (b) Number i Units

Answer 1

red blue o=50° no=1527 ; n = 1518 rol sino =) Singa o nb Sino =0.5017 = %= 30.10 sino sino Sing= nr .=) Sindo, = 1.5184 Sin 30.3 = So, 249.980 @ Inside the pane. Sino for blue, no Sinab Sin so 1.527 for red, Nya Sing Sing= sinso The angular spread for blue, nya Sind for red, n = Sin Sri sonry 0 1.518 =0.5046 = 8 = 6 = 30.30 when light enters the pane = %= %= 30.3-30.1= 0.2 (b) when light emerges from opposite side: Sino =) Sind = 1.527 x Sin 30.1 => 8, 249:98° The angular spread when light emerges from the opposite side =%, 86, = 49.98 - 49.98=0.00 (0) 90 n = 1.58 M₂ = 150. Let c be the costical angle for plastie core- plastic sheath interface -0.9494 =) Ca sos!(0.9494) >> C=717° 1.50 Sinca M2 ni 1:58 Using shell's law, sino - nix Singo - 158x Sin77 Sino=n,x Sino 8290-c=90-7117=18.30 21:58xsin 18.3= 0.4961 =) O= sin "(0.4961)=29.70 The maximum value of 8 = 29.7°