Snell's law of refraction can be written as sin i = n sin r, where n is the refractive index from air to water, i is the angle of incidence, and r is the angle of refraction.
In an experiment where a ray of light is directed from air into water, if the angle of incidence is 46 degrees, choose 1 option which gives the angle of refraction predicted by Snell's law, correct to 2 significant figures, given that n = 1.208.
A) 0.84 degrees
B) 0.85 degrees
C) 23 degrees
D) 36 degrees
E) 37 degrees
F) 45 degrees
G) 46 degrees
H) 47 degrees
Can anyone help please?
For Further Reading
math - Reiny, Monday, May 14, 2007 at 12:45pm
have you tried substituting your given values in the given formula?
The correct answer is obtained in one step.
math - HALEY, Monday, May 14, 2007 at 8:22pm
1 STEP
Is the answer E? 37 degree?
yes it is.
36.55º which to 2 significant figures is 37º.
To solve this problem, we need to use Snell's law of refraction, which states that sin i = n sin r, where n is the refractive index, i is the angle of incidence, and r is the angle of refraction.
Given that n = 1.208, and the angle of incidence is 46 degrees, we need to find the angle of refraction.
Substituting the values into the equation, we have sin 46 = 1.208 sin r.
To solve for r, we first isolate sin r by dividing both sides of the equation by 1.208:
sin r = (sin 46) / 1.208.
Now we can solve for r by taking the inverse sine (or arcsine) of both sides of the equation:
r = arcsin((sin 46) / 1.208).
Using a calculator, we find that r = 36.55 degrees.
However, we need to round our answer to 2 significant figures. Rounding 36.55 to 2 significant figures gives us 37 degrees.
Therefore, the correct answer is option E) 37 degrees.