What will the angle of refraction be for a ray of light passing from air into a sodium chloride crystal, if the angle of incidence is 60.0°? The index of refraction of sodium chloride is 1.53.
What will the angle of refraction be for a ray of light passing from air into a sodium chloride crystal if the angle of incidence is 60.0°? The index of refraction of sodium chloride is 1.53.
What will the angle of refraction be for a ray of light passing from air into a sodium chloride crystal, if the angle of incidence is 60.0°? The index of refraction of sodium chloride is 1.53
To find the angle of refraction when light passes from air into a sodium chloride crystal, we can use Snell's law. Snell's law states that:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ = index of refraction of the initial medium (air)
n₂ = index of refraction of the final medium (sodium chloride)
θ₁ = angle of incidence
θ₂ = angle of refraction
Given:
n₁ (air) = 1.00 (approximate index of refraction for air)
n₂ (sodium chloride) = 1.53
θ₁ (angle of incidence) = 60.0°
Let's calculate the angle of refraction using Snell's law:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
1.00 * sin(60.0°) = 1.53 * sin(θ₂)
Solving for sin(θ₂):
sin(θ₂) = (1.00 * sin(60.0°)) / 1.53
sin(θ₂) ≈ 0.649
Now, we can find the angle θ₂ by taking the inverse sine (arcsine) of both sides:
θ₂ ≈ arcsin(0.649)
Using a calculator, we find:
θ₂ ≈ 39.3°
Therefore, the angle of refraction for a ray of light passing from air into a sodium chloride crystal with an angle of incidence of 60.0° is approximately 39.3°.
To find the angle of refraction, we can use Snell's law, which relates the angle of incidence (θᵢ) and the angle of refraction (θₑ) to the indices of refraction of the two media involved.
Snell's law states:
n₁ × sin(θᵢ) = n₂ × sin(θₑ)
where n₁ is the index of refraction of the initial medium (air) and n₂ is the index of refraction of the final medium (sodium chloride crystal).
Given:
θᵢ = 60.0°
n₂ = 1.53
Step 1: Convert the angle from degrees to radians.
θᵢ(radians) = θᵢ(degrees) × (π/180)
θᵢ(radians) = 60.0° × (π/180)
θᵢ(radians) = 1.0472 radians (approx.)
Step 2: Apply Snell's law to find θₑ.
n₁ × sin(θᵢ) = n₂ × sin(θₑ)
Air has an index of refraction very close to 1, so we can assume n₁ = 1.
1 × sin(1.0472) = 1.53 × sin(θₑ)
sin(1.0472) = 1.53 × sin(θₑ)
Step 3: Solve for θₑ.
θₑ = arcsin(sin(1.0472) / 1.53)
Using a calculator, we find that θₑ = 0.6785 radians (approx.).
Step 4: Convert θₑ back to degrees.
θₑ(degrees) = θₑ(radians) × (180/π)
θₑ(degrees) = 0.6785 × (180/π)
θₑ(degrees) = 38.9° (rounded to one decimal place)
Therefore, the angle of refraction is approximately 38.9°.