Answer:
Red light has an angle of refraction of 48.3°.
Violet light has an angle of refraction of 47.8°.
Explanation:
From Snell's law of refraction, the refractive index is the ratio of the sine of the angle of incidence to the sine of the angle of refraction.
[tex]n=\dfrac{\sin i}{\sin r}[/tex]
For red light in water,
[tex]1.331=\dfrac{\sin 84}{\sin r}[/tex]
[tex]\sin r=\dfrac{\sin 84}{1.331}=0.7472[/tex]
[tex]r=\sin^{-1}0.7472=48.3}[/tex]
For violet light in water,
[tex]1.342=\dfrac{\sin 84}{\sin r}[/tex]
[tex]\sin r=\dfrac{\sin 84}{1.342}=0.7411[/tex]
[tex]r=\sin^{-1}0.7411=47.8}[/tex]
The angle at which the light got refracted is known as the angle of refraction. The angle of refraction of red light is 48.3°. While the angle of refraction of Violet light is 47.8°.
"The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given color and for a given set of media,
According to Snell's law. The formula for Snell's law is
[tex]\rm {n= \frac{sini}{sinr} }[/tex]
i is the incidence angle
r is the refraction angle.
n is the refractive index of the medium
For red light,
[tex]\rm {n= \frac{sini}{sinr} }\\\\\rm {1.331= \frac{sin84^0}{sinr}\\[/tex]
[tex]\rm{sinr=\frac{sin84^0}{1.331}}[/tex]
[tex]\rm r = sin^{-1}(0.7472)[/tex]
[tex]\rm r = 48.3^0[/tex][tex]\rm r = 47.8^0[/tex]
Hence the angle of refraction of red light is 48.3
For violet light,
[tex]\rm {n= \frac{sini}{sinr} }\\\\\rm {1.342= \frac{sin84^0}{sinr}\\[/tex]
[tex]\rm{sinr=\frac{sin84^0}{1.342}}[/tex]
[tex]r = sin^{-1}(0.7411)[/tex]
Hence the angle of refraction of Violet light is 47.8°.
To learn more about snell's law refer to the link;
https://brainly.com/question/10112549
