Refraction and Snell’s law

Refraction and Snell’s law

Lessons

In this lesson, we will learn:

  • Meaning of refractive index
  • Snell’s law
  • Calculating speed of light and angle of refraction in different media

Notes:

  • When light travels from one medium to another, the light is refracted: the direction of the light changes. This change in direction is caused by differences in the speed of light as it travels through different media:
    • When light travels from a medium where it moves faster to a medium where it moves slower, the light is refracted towards the normal.
    • When light travels from a medium where it moves slower to a medium where it moves faster, the light is refracted away from the normal.
  • Refractive index (n) is a unitless quantity associated with a medium that describes how much that medium refracts lights (i.e. a material possessing a larger refractive index indicates a greater change in the direction of light). When light passes from one medium to another, Snell’s law relates the refractive indices of the two media to the angle of incidence and angle of refraction of the light:
  • Snell’s law angle of incidence angle of refraction
    In the above diagram, θ\theta 1 is the angle of incidence and θ\theta 2 is the angle of refraction. These angles are measured from the ray of light to the normal, a line that is perpendicular to the surface of the new medium.
  • The refractive index is also related to the speed of light inside the medium by the following expression:

  • n = cv\large \frac{c}{v}

    We can see in the above expression that n is inversely proportional to v (i.e. light travels slower in media with larger n). Therefore, the above relationships between v and the direction light bends in can be restated in terms of n:
    • When light travels from a medium with lower n (faster) to a medium with higher n (slower), the light is refracted towards the normal.
    • When light travels from a medium with higher n (slower) to a medium with lower n (faster), the light is refracted away from the normal.

Index of Refraction

n = cv\large \frac{c}{v}

n: Index of refraction of medium, unitless

c: Speed of light in a vacuum, in meters per second (m/s)

v: Speed of light inside medium, in meters per second (m/s)


Snell’s Law

n1 sin(θ\theta 1) = n2 sin(θ\theta 2)

n1, n2: Index of refraction of medium, unitless

θ\theta 1, θ\theta 2: Angle from normal in each medium, in degrees (°)


Speed of Light

c = 3.00 × 108 m/s
  • 1.
    Refractive index and Snell's law
    A light ray travels from air (n = 1.00) into a sheet of transparent plastic at an angle of incidence of 40.0°. The light ray refracts at an angle of refraction of 22.9°.

    Refractive index and Snell's law  angle of incidence angle of refraction
    a)
    What is the index of refraction of the plastic?

    b)
    What is the speed of the light ray inside the plastic?


  • 2.
    Snell's law with layers of different media
    A light ray travels from air (n = 1.00) into a sheet of diamond (n = 2.42) with an angle of incidence of 25.0°. It passes through a second layer of acrylic (n = 1.49), then back into air. What is the angle of refraction:

    Snell's law with layers of different media  angle of incidence angle of refraction


    1. In diamond?
    2. In acrylic?
    3. In air, when it comes out the other side?

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