Refraction
Waves - OCR A-Level Physics
Key Definition
Refraction
The change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. The frequency remains constant; the wavelength changes.
The change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. The frequency remains constant; the wavelength changes.
- When light enters a denser medium (higher refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium.), it slows down and bends towards the normal.
- When light enters a less dense medium, it speeds up and bends away from the normal.
- Refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. n of a material: $n = c/v$, where c is the speed of light in a vacuum and v is the speed in that material. n is always ≥ 1.
$$n_{1} \sin\theta_{1} = n_{2} \sin\theta_{2}$$
Key Definition
Total internal reflection
When light travelling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle, all the light is reflected back into the denser medium.
When light travelling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle, all the light is reflected back into the denser medium.
Key Definition
Critical angle (θ_c)
The angle of incidence at which the angle of refraction is exactly 90°. At this angle, the refracted ray travels along the boundary.
The angle of incidence at which the angle of refraction is exactly 90°. At this angle, the refracted ray travels along the boundary.
$$\sin\theta_{c} = \frac{n_{2}}{n_{1}}$$
- For a glass–air boundary: sin θ_c = 1/n_glass (since n_air ≈ 1).
- Two conditions for TIR: (1) light must travel from a denser to a less dense medium, (2) the angle of incidence must exceed the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs..
- Applications: optical fibresThin glass strands that transmit light by total internal reflection, used in communications and medical endoscopy. use TIR to transmit light signals over long distances with minimal loss.
Worked Example [3 marks]
Glass has a refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. of 1.52. Calculate the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs. for a glass–air boundary.
Show Solution
1
Use sin $\theta_{c} = n_{2}/n_{1} = 1.00/1.52$
[1]2
sin $\theta_{c} = 0.6579$
[1]3
$\theta_c = sin⁻¹(0.6579) = 41.1°$
[1]Answer
$\theta_c = 41.1°$
Common Mistake
MEDIUM
Students often: Writing sin $\theta_{c} = n_{1}/n_{2}$ instead of sin $\theta_{c} = n_{2}/n_{1} (putting$ the denser medium on top).
Instead: The less dense medium (smaller n) always goes on top: sin θ_c = n_less dense / n_more dense. For glass–air: sin $\theta_{c} = 1/n_{\text{glass}}$.
Instead: The less dense medium (smaller n) always goes on top: sin θ_c = n_less dense / n_more dense. For glass–air: sin $\theta_{c} = 1/n_{\text{glass}}$.