Explanation:
Below is an attachment containing the solution.
Answer
given,
wavelength of red light = 660 nm
wavelength of blue light = 470 nm
thickness = 1 cm = 0.01 m
angle of incident = 30°
using Snell's law
n₁ sin θ₁ = n₂ sin θ₂
refractive index for red and blue color for crown glass
n_r = 1.512 n_b = 1.524
now,
incident ray is red
![sin (\theta_{ir})=\dfrac{1\times sin(30^0)}{1.512}](https://tex.z-dn.net/?f=sin%20%28%5Ctheta_%7Bir%7D%29%3D%5Cdfrac%7B1%5Ctimes%20sin%2830%5E0%29%7D%7B1.512%7D)
when incident ray is blue
![sin (\theta_{ib})=\dfrac{1\times sin(30^0)}{1.524}](https://tex.z-dn.net/?f=sin%20%28%5Ctheta_%7Bib%7D%29%3D%5Cdfrac%7B1%5Ctimes%20sin%2830%5E0%29%7D%7B1.524%7D)
so,
![(\theta_e)_r=sin^{-1}(\dfrac{1.512 sin (\theta_{ir})}{1})](https://tex.z-dn.net/?f=%28%5Ctheta_e%29_r%3Dsin%5E%7B-1%7D%28%5Cdfrac%7B1.512%20sin%20%28%5Ctheta_%7Bir%7D%29%7D%7B1%7D%29)
![(\theta_e)_r=sin^{-1}(\dfrac{1.512\times \dfrac{1\times sin(30^0)}{1.512}}{1})](https://tex.z-dn.net/?f=%28%5Ctheta_e%29_r%3Dsin%5E%7B-1%7D%28%5Cdfrac%7B1.512%5Ctimes%20%5Cdfrac%7B1%5Ctimes%20sin%2830%5E0%29%7D%7B1.512%7D%7D%7B1%7D%29)
on solving
![(\theta_e)_r = 30^0](https://tex.z-dn.net/?f=%28%5Ctheta_e%29_r%20%3D%2030%5E0)
similarly for blue ray the angle of emerge is 30°
b)
now, refracting angle of blue and red ray
![sin (\theta_{ir})=\dfrac{1\times sin(30^0)}{1.512}](https://tex.z-dn.net/?f=sin%20%28%5Ctheta_%7Bir%7D%29%3D%5Cdfrac%7B1%5Ctimes%20sin%2830%5E0%29%7D%7B1.512%7D)
![\theta_{ir}=19.316^0](https://tex.z-dn.net/?f=%5Ctheta_%7Bir%7D%3D19.316%5E0)
for blue ray
![sin (\theta_{ib})=\dfrac{1\times sin(30^0)}{1.524}](https://tex.z-dn.net/?f=sin%20%28%5Ctheta_%7Bib%7D%29%3D%5Cdfrac%7B1%5Ctimes%20sin%2830%5E0%29%7D%7B1.524%7D)
![\theta_{ib}=19.158^0](https://tex.z-dn.net/?f=%5Ctheta_%7Bib%7D%3D19.158%5E0)
now,
d₁ = 1 x tan(19.316°) = 0.3505 m
d₂ = 1 x tan (19.158°) = 0.3474 m
now, the distance is separated by
Δ d = d₁ - d₂
Δ d = 0.3505 - 0.3474
Δ d =0.0031 cm
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