Final answer:
To determine the index of refraction of the unknown substance, Snell's law is applied using the given incident angle and observed angle of refraction. By performing the calculations, the index of refraction is found to be approximately 1.43, which could indicate the substance is a type of glass or plastic.
Step-by-step explanation:
To find the index of refraction of the unknown substance using the information provided (incident angle of 45.0° and the angle of refraction of 40.3° in water), we need to apply Snell's law, which states:
n1 · sin(θ1) = n2 · sin(θ2)
Where:
- n1 is the refractive index of water (1.33)
- θ1 is the incident angle in water (45.0°)
- θ2 is the angle of refraction in the substance (40.3°)
and n2 is the refractive index of the unknown substance, which is what we're solving for.
Plugging our known values into Snell's law:
1.33 · sin(45.0°) = n2 · sin(40.3°)
First, calculate the sine of both angles:
sin(45.0°) = 0.7071
sin(40.3°) = 0.6561
Now, plug the sine values into Snell's law and solve for n2:
1.33 · 0.7071 = n2 · 0.6561
0.9394 = n2 · 0.6561
Dividing both sides by 0.6561 gives us:
n2 = 0.9394 / 0.6561 ≈ 1.43
The index of refraction of the substance is approximately 1.43, which could suggest the substance is a certain type of glass or plastic.