Angle of refraction of light in water

[Kaldanis]

Homework Statement

A ray of pure yellow light reaches the surface of a pond at an angle of incidence of 60°. What angle does it make with the normal inside the water?

Speed of light in air = 300,000,000 m/s
Speed of light in water = 225,000,000 m/s
So the Refractive index μ = 1.33

Homework Equations

μ = angle of incidence / angle of refraction

The Attempt at a Solution

μ = sin i / sin r
1.33 = 60° / sin r
sin r = 60° / 1.33

So the angle of refraction equals 45.11°. Is this correct? I believe this is the correct way to work it out, yet when I check the answer online using various calculators the answer comes up as 40.62°. Am I doing something wrong?

 

[HallsofIvy]

Homework Statement

A ray of pure yellow light reaches the surface of a pond at an angle of incidence of 60°. What angle does it make with the normal inside the water?

Speed of light in air = 300,000,000 m/s
Speed of light in water = 225,000,000 m/s
So the Refractive index μ = 1.33

Homework Equations

μ = angle of incidence / angle of refraction

The Attempt at a Solution

μ = sin i / sin r
1.33 = 60° / sin r
sin r = 60° / 1.33

So the angle of refraction equals 45.11°. Is this correct? I believe this is the correct way to work it out, yet when I check the answer online using various calculators the answer comes up as 40.62°. Am I doing something wrong?

yes, you are. And the problem is shown in your writing "μ = angle of incidence / angle of refraction" when it should be "μ = sin(angle of incidence) / sin(angle of refraction)"

You write that below but then you write "1.33= 60°/ sin r" and "sin r= 60°/1.33= 45.11°"

sin r= sin(60°)/1.33. Use a calculator to determine sin(60°) and once you have sin r, use a calculator again to determine r itself.

 

[Kaldanis]

yes, you are. And the problem is shown in your writing "μ = angle of incidence / angle of refraction" when it should be "μ = sin(angle of incidence) / sin(angle of refraction)"

You write that below but then you write "1.33= 60°/ sin r" and "sin r= 60°/1.33= 45.11°"

sin r= sin(60°)/1.33. Use a calculator to determine sin(60°) and once you have sin r, use a calculator again to determine r itself.

Ah, I see now. Sin r = 0.6511469, so r = 40.62°

Thank you sir!