Sure! Let's solve this step-by-step using Snell's Law.
### Step-by-Step Solution:
1. Identify the Given Values:
- Angle of incidence ([tex]\( \theta_1 \)[/tex]): 35 degrees
- Refractive index of water ([tex]\( n_1 \)[/tex]): 1.33
- Refractive index of air ([tex]\( n_2 \)[/tex]): 1.00
2. Convert Angle of Incidence to Radians:
Since calculations with trigonometric functions commonly use radians, we convert 35 degrees to radians:
[tex]\[
\theta_1 = 35^\circ \approx 0.6108652381980153 \text{ radians}
\][/tex]
3. Apply Snell's Law:
Snell's Law states that:
[tex]\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\][/tex]
We need to solve for the angle of refraction ([tex]\( \theta_2 \)[/tex]).
4. Calculate [tex]\( \sin(\theta_2) \)[/tex]:
Rearrange Snell's Law to solve for [tex]\( \sin(\theta_2) \)[/tex]:
[tex]\[
\sin(\theta_2) = \frac{n_1 \sin(\theta_1)}{n_2}
\][/tex]
Substitute the values:
[tex]\[
\sin(\theta_2) = \frac{1.33 \sin(0.6108652381980153)}{1.00} \approx 0.7628566603468913
\][/tex]
5. Find [tex]\( \theta_2 \)[/tex] in Radians:
To find the angle of refraction in radians, we take the inverse sine (arcsine) of [tex]\( \sin(\theta_2) \)[/tex]:
[tex]\[
\theta_2 \approx \arcsin(0.7628566603468913) \approx 0.867719865780809 \text{ radians}
\][/tex]
6. Convert the Angle of Refraction to Degrees:
Convert [tex]\( \theta_2 \)[/tex] from radians to degrees:
[tex]\[
\theta_2 \approx 49.716686108898614^\circ
\][/tex]
Thus, the angle of refraction when a light ray passes from water into the air with an angle of incidence of 35 degrees is approximately [tex]\( 49.72^\circ \)[/tex].
