A ray of light passes from air into water. The incident angle is 30o. Find the index of refraction of water if the angle of refraction is 22o.
Ans. 1.333
N1SinQ1=N2SinQ2
1*Sin30=N2Sin(22)
Sin(30)/sin(22)=N2
1.33=N2
To find the index of refraction of water, we can use Snell's law. Snell's law relates the incident angle and the angle of refraction to the indices of refraction of the two mediums. The formula for Snell's law is:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
n1 = index of refraction of the first medium (in this case, air)
theta1 = angle of incidence
n2 = index of refraction of the second medium (in this case, water)
theta2 = angle of refraction
Given:
theta1 = 30 degrees
theta2 = 22 degrees
We can rearrange the formula to solve for n2:
n2 = (n1 * sin(theta1)) / sin(theta2)
Since the index of refraction of air is approximately 1, we substitute n1 = 1 and plug in the values:
n2 = (1 * sin(30)) / sin(22)
Using a calculator, we find:
n2 ≈ 1.333
So, the index of refraction of water is approximately 1.333.
To find the index of refraction of water, we can use Snell's Law. Snell's Law states that the ratio of the sines of the incident angle to the angle of refraction is equal to the ratio of the indices of refraction of the two mediums.
The equation for Snell's Law is:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
where:
n₁ = index of refraction of the first medium (air)
θ₁ = incident angle
n₂ = index of refraction of the second medium (water)
θ₂ = angle of refraction
Given:
θ₁ = 30°
θ₂ = 22°
We know that the index of refraction of air is approximately 1.
Plugging in the known values into Snell's Law, we have:
1 * sin(30°) = n₂ * sin(22°)
Now, let's solve for n₂:
sin(30°) / sin(22°) = n₂
Using a calculator, we find:
n₂ ≈ 1.333
Therefore, the index of refraction of water is approximately 1.333.