a ray of light in air enters a glass surface at right angles to the surface. what is the angle of refraction
zero
When a ray of light passes from one medium to another, it changes direction due to a phenomenon called refraction. The angle of incidence (i) and the angle of refraction (r) are related by Snell's law:
n₁ sin(i) = n₂ sin(r)
Where:
- n₁ is the refractive index of the first medium (in this case, air),
- n₂ is the refractive index of the second medium (in this case, glass),
- sin(i) is the sine of the angle of incidence, and
- sin(r) is the sine of the angle of refraction.
Since the ray of light enters the glass surface at right angles (i.e., the angle of incidence is 90 degrees), the sine of the angle of incidence will be equal to 1.
Snell's law simplifies to:
n₁ = n₂ sin(r)
Since we are considering air and glass, we can approximate the refractive index of air as 1.00 and look up the refractive index of the glass material in question.
For example, the refractive index of common crown glass is approximately 1.52. Using this value, we can find the angle of refraction using Snell's law:
1.00 = 1.52 sin(r)
Rearranging the equation to solve for sin(r):
sin(r) = 1.00 / 1.52
Taking the inverse sine of this value will give us the angle of refraction:
r = sin^(-1)(1.00 / 1.52)
Using a calculator, the angle of refraction is approximately 41 degrees.
To determine the angle of refraction, we can use Snell's Law, which relates the angles of incidence and refraction of light as it passes from one medium to another. Snell's Law states that the ratio of the sine of the angle of incidence (θ₁) to the sine of the angle of refraction (θ₂) is equal to the ratio of the velocities of light in the two media.
When light passes from air into glass, the refractive index of air is approximately 1, while the refractive index of glass is typically around 1.5.
Since the angle of incidence (θ₁) is given as "at right angles to the surface," it means the light ray is incident perpendicular to the air-glass interface. In this case, the angle of incidence will be 0 degrees.
Using Snell's Law:
sin(θ₁) / sin(θ₂) = n₂ / n₁
Plugging in the values:
sin(0°) / sin(θ₂) = 1.5 / 1
Since sin(0°) is 0, we have:
0 / sin(θ₂) = 1.5 / 1
To solve for sin(θ₂), we can cross-multiply:
0 * 1 = sin(θ₂) * 1.5
Thus, sin(θ₂) = 0, resulting in θ₂ = 0°.
Therefore, the angle of refraction when a ray of light enters a glass surface at right angles to the surface is 0 degrees.