Respuesta :
Answer:
(a) 1.5
(b) [tex]421.86 * 10^{-9} m[/tex]
Explanation:
Angle of incidence, [tex]i[/tex] = 29.8°
Angle of refraction, [tex]r[/tex] = 18.62°
(a) Index of refraction is given as:
[tex]n = \frac{sin(i)}{sin(r)}[/tex]
[tex]n = \frac{sin(29.8)}{sin(18.62)} \\\\\\n = \frac{0.4970}{0.3193} \\\\\\n = 1.5[/tex]
The refractive index of the syrup is 1.5.
(b) Wavelength of the red light in a vacuum, λ(1) = [tex]632.8 nm = 632.8 * 10^{-9} m[/tex]
Refractive index is also a ratio of the speed of the light in a vacuum with the speed of light in a particular medium:
[tex]n = \frac{c}{v}[/tex]
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 = [tex]632.8 * 10^{-9}[/tex] / λ(2)
The wavelength of the red light in the solution is therefore:
λ(2) = [tex]632.8 * 10^{-9}[/tex] / 1.5
λ(2) = [tex]421.86 * 10^{-9} m[/tex]
The wavelength of the light in the solution is [tex]421.86 * 10^{-9} m[/tex]
