What is the critical angle of light traveling from benzene (n=1.501) into air?
Choose one answer.
a. 40.05o
b. 48.22o
c. 41.78o
d. 62.63o
its 41.78 Degrees
The critical angle is sin^-1(1/n)
= _____
Larger angles of incidence from inside the benzene experience total internal reflection.
You do the calculation
To find the critical angle of light traveling from benzene into air, we can use Snell's law. Snell's law relates the incident angle (θ₁) and the refracted angle (θ₂) to the refractive indices of the two media.
Snell's law states: n₁ * sin(θ₁) = n₂ * sin(θ₂)
The critical angle occurs when the refracted angle is 90 degrees. Thus, sin(θ₂) = sin(90°) = 1.
Let's plug in the values:
n₁ (refractive index of benzene) = 1.501
n₂ (refractive index of air) = 1 (approximately)
n₁ * sin(θ₁) = n₂ * sin(90°)
1.501 * sin(θ₁) = sin(90°)
sin(θ₁) = sin(90°) / 1.501
sin(θ₁) = 0.666222
To find the angle θ₁, we can take the inverse sine (sin⁻¹) of 0.666222:
θ₁ ≈ sin⁻¹(0.666222) ≈ 41.78°
Therefore, the critical angle of light traveling from benzene into air is approximately 41.78°.
So, the correct answer is c. 41.78°.
To find the critical angle of light traveling from benzene into air, we can apply Snell's law. Snell's law relates the angles of incidence and refraction as well as the refractive indices of the two media involved. The critical angle occurs when the angle of refraction is 90 degrees, causing the refracted ray to be parallel to the surface.
The formula for Snell's law is:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ = refractive index of the initial medium (benzene)
θ₁ = angle of incidence
n₂ = refractive index of the final medium (air)
θ₂ = angle of refraction
In this case, we are trying to find the critical angle, which means the angle of refraction is 90 degrees. Therefore, we can rearrange the equation to solve for the angle of incidence:
sin(θ₁) = (n₂ / n₁) * sin(θ₂)
Since sin(90 degrees) is 1, the equation becomes:
sin(θ₁) = (n₂ / n₁)
Now we can substitute the given values:
n₁ (refractive index of benzene) = 1.501
n₂ (refractive index of air) = 1.000
sin(θ₁) = (1.000 / 1.501)
To find the critical angle, we need to find the angle whose sine is equal to (1.000 / 1.501). We can use an inverse sine function (also known as arcsine) to find this angle.
θ₁ = arcsin(1.000 / 1.501)
Using a calculator, the value of θ₁ is approximately 41.78 degrees.
Therefore, the correct answer is c. 41.78o.