Answer:
(a) 1.5
(b) ![421.86 * 10^{-9} m](https://tex.z-dn.net/?f=421.86%20%2A%2010%5E%7B-9%7D%20m)
Explanation:
Angle of incidence,
= 29.8°
Angle of refraction,
= 18.62°
(a) Index of refraction is given as:
![n = \frac{sin(i)}{sin(r)}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7Bsin%28i%29%7D%7Bsin%28r%29%7D)
![n = \frac{sin(29.8)}{sin(18.62)} \\\\\\n = \frac{0.4970}{0.3193} \\\\\\n = 1.5](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7Bsin%2829.8%29%7D%7Bsin%2818.62%29%7D%20%5C%5C%5C%5C%5C%5Cn%20%3D%20%5Cfrac%7B0.4970%7D%7B0.3193%7D%20%5C%5C%5C%5C%5C%5Cn%20%3D%201.5)
The refractive index of the syrup is 1.5.
(b) Wavelength of the red light in a vacuum, λ(1) = ![632.8 nm = 632.8 * 10^{-9} m](https://tex.z-dn.net/?f=632.8%20nm%20%3D%20632.8%20%2A%2010%5E%7B-9%7D%20m)
Refractive index is also a ratio of the speed of the light in a vacuum with the speed of light in a particular medium:
![n = \frac{c}{v}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7Bc%7D%7Bv%7D)
The speed of light in a vacuum is given as;
c = λ(1) * f
=> f = c/λ(1)
The speed of light in a medium is given as;
v = λ(2) * f
=> f = v/λ(2)
(λ = wavelength and f = frequency)
We know that the frequency of light does not change when it changes media, hence, we can equate both frequencies:
c/λ(1) = v/λ(2)
Therefore:
c / v = λ(1) / λ(2)
Therefore, refractive index will become:
n = λ(1) / λ(2)
=> 1.5 =
/ λ(2)
The wavelength of the red light in the solution is therefore:
λ(2) =
/ 1.5
λ(2) = ![421.86 * 10^{-9} m](https://tex.z-dn.net/?f=421.86%20%2A%2010%5E%7B-9%7D%20m)
The wavelength of the light in the solution is ![421.86 * 10^{-9} m](https://tex.z-dn.net/?f=421.86%20%2A%2010%5E%7B-9%7D%20m)