Refraction Using Huygens' Principle
Refraction by Huygens' principle explains the bending of a plane wavefront at a boundary because light travels with different speeds in two media, leading to the relation n1 sin θ1 = n2 sin θ2.
In one line: Same medium, same pair: n1 with θ1, n2 with θ2.
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When one end of an incident wavefront reaches the second medium earlier than the other end, that part begins to travel with the speed of the second medium while the remaining part is still in the first medium. The change in speed changes the direction of the refracted wavefront. Rays drawn normal to the incident and refracted wavefronts give the incident and refracted ray directions.
Example
Formula and rule
Assumptions: the incident wavefront is plane, the boundary is plane, and light speeds are v1 and v2 in the two media.
Geometry gives sin θ1 / sin θ2 = v1 / v2.
Using n = c/v, this becomes n1 sin θ1 = n2 sin θ2.
Here n1 and n2 have no SI unit, while v1 and v2 are in m s−1 and θ1, θ2 are measured from the normal.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
Light travels from air, n1 = 1.00, into glass, n2 = 1.50, at θ1 = 30 degree.
- 1Using n1 sin θ1 = n2 sin θ2: 1.00 x sin 30 degree = 1.50 x sin θ2.
- 2So sin θ2 = 0.50/1.50 = 0.333 and θ2 = 19.5 degree.
- 3If c = 3.0 × 108 m s−1, the speed in glass is v2 = c/n2 = 2.0 × 108 m s−1, confirming that the ray bends towards the normal because light slows down.
Method you can reuse
- 1Start with a plane wavefront incident on a plane boundary.
- 2Mark the point that reaches the second medium first, draw its secondary wavelet of radius v2t in the second medium, and mark the distance v1t travelled by the other end in the first medium during the same time.
- 3Draw the refracted wavefront as the tangent to the secondary wavelet.
- 4Use the two right triangles to obtain sin θ1 / sin θ2 = v1 / v2, then substitute n = c/v to get n1 sin θ1 = n2 sin θ2.
Sketch it in your answer
Draw a plane boundary, normal at the point of incidence, incident wavefront, refracted wavefront, incident ray and refracted ray. Label θ1 and θ2 with respect to the normal, and show different wave speeds v1 and v2.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why does a wavefront change direction when it passes from air into glass?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is n2 sin θ1 = n1 sin θ2, caused by interchanging media. Keep the refractive index with the sine of the angle in the same medium.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Refraction by Huygens' principle explains the bending of a plane wavefront at a boundary because light travels with different speeds in two media, leading to the relation n1 sin θ1 = n2 sin θ2.
- 2
Add for 2 marks
Example: When light enters glass from air, its speed decreases. The refracted ray bends towards the normal, and the refracted wavefront changes orientation accordingly.
- 3
Add for 3 marks
When one end of an incident wavefront reaches the second medium earlier than the other end, that part begins to travel with the speed of the second medium while the remaining part is still in the first medium.
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