The Human Eye and the Colourful World · Lesson 4 of 8
Refraction of Light Through a Prism
“Two tilted surfaces send one light ray away with a brand-new direction.”
• Describe the structure and refracting surfaces of a triangular glass prism. • Trace a light ray through both faces of a prism. • Identify the angles of incidence, refraction, emergence, prism and deviation. • Explain why a prism changes the direction of the emergent ray. • Compare refraction through a prism with refraction through a rectangular glass slab. • Carry out a pin-tracing activity to determine the ray path through a prism.
A ray passing through a rectangular glass slab bends at both surfaces, yet the emergent ray is parallel to the incident ray. Replace the slab with a triangular prism and this convenient cancellation disappears. The two refracting surfaces are inclined to each other, so the second bend does not restore the original direction. The result is a clearly deviated emergent ray.
A triangular glass prism has two triangular bases and three rectangular lateral surfaces. Light is commonly sent through two of the rectangular faces. The angle between these two refracting faces is called the angle of the prism. Because these faces are not parallel, their normals are also not parallel.
The angle between the two inclined lateral faces of a prism through which refraction takes place.
The Ray Path Through A Prism
At the first face, the ray travels from air into glass. Glass is optically denser than air, so the ray bends towards the normal. It then travels inside the prism as the refracted ray. At the second face, it travels from glass into air and bends away from the normal. Each bending follows the familiar rule for the direction of refraction, but the inclined faces make their combined effect different from that of a slab.
The incoming line is the incident ray, the line inside the prism is the refracted ray and the outgoing line is the emergent ray. The angle between the incident ray and the normal at the first face is the angle of incidence, i. The angle between the refracted ray and that normal is the angle of refraction, r. At the second face, the angle between the emergent ray and the second normal is the angle of emergence, e.
The angle between the original direction of the incident ray, produced forward, and the direction of the emergent ray after it passes through the prism.
To locate the deviation, extend the original incident direction in a straight line beyond the prism and compare it with the emergent ray. The angle between these directions is D, the angle of deviation. It describes the net change in direction caused by both refractions; it is not the same as the angle of emergence or the angle of the prism.
| Symbol or ray | Meaning | Where it is identified |
|---|---|---|
| PE | Incident ray | Before the first prism face |
| EF | Refracted ray | Inside the prism |
| FS | Emergent ray | After the second prism face |
| i | Angle of incidence | Between incident ray and first normal |
| r | Angle of refraction | Between refracted ray and first normal |
| e | Angle of emergence | Between emergent ray and second normal |
| A | Angle of the prism | Between the two refracting faces |
| D | Angle of deviation | Between incident direction produced and emergent ray |
Prism And Rectangular Glass Slab
In a rectangular slab, the entry and exit faces are parallel. The ray bends towards the normal at entry and away from the normal at exit by matching geometry. It emerges parallel to its original direction but shifted sideways; this shift is lateral displacement. In a prism, the corresponding faces are inclined. The second bend occurs relative to a differently directed normal, so the emergent ray is not parallel to the incident ray.
Problem
A ray enters a glass prism from air. In which direction does it bend at the first face?
- 1.Identify the change of medium: air to glass.
- 2.The ray enters an optically denser medium.
- 3.Therefore it bends towards the normal at the first face.
- 4.The angle of refraction in glass is smaller than the angle of incidence for this transition.
Problem
A ray inside a prism reaches the second face and enters air. Predict its bending and explain why the emergent ray may still be deviated overall.
- 1.The transition is glass to air, from optically denser to optically rarer medium.
- 2.The ray bends away from the normal at the second face.
- 3.The second normal is not parallel to the first normal because the prism faces are inclined.
- 4.Therefore the two bends do not cancel, and the emergent ray remains at an angle to the original incident direction.
Problem
A diagram labels the angle between the emergent ray and the second normal as D. Is the label correct?
- 1.The angle between the emergent ray and the second normal is the angle of emergence, e.
- 2.The angle of deviation, D, must be measured between the emergent ray and the original incident direction produced forward.
- 3.Therefore the label is incorrect and should be replaced by e; D must be moved to the angle between the two ray directions.
Activity
Purpose: To trace the path of a light ray through a triangular glass prism and measure its main angles. Materials: A triangular glass prism, white paper, drawing board, drawing pins, four optical pins, pencil, ruler and protractor.
• Fix the paper to the drawing board and place the prism on its triangular base. Trace its outline. • Draw a straight line PE inclined to the first refracting face and fix two pins P and Q vertically on it. • Looking through the second face, place pins R and S so that they appear in one straight line with the images of P and Q. Keep the pins well separated for accurate alignment. • Remove the pins and prism. Join the pin points to locate the incident and emergent paths, and join the points where the ray enters and leaves the prism. • Draw a normal at each refracting face. Mark i, r, e, A and D with a protractor.
Observation: The ray bends towards the normal on entering glass and away from the normal on leaving it. The emergent ray is not parallel to the incident ray produced forward. Explanation: The inclined faces have differently directed normals, so the two refractions produce a net angular change. Conclusion: A triangular prism deviates light.
Use thin pencil lines, keep pins vertical, place each pair several centimetres apart and avoid moving the prism after tracing its outline. Measure every angle from the appropriate normal, not from the prism surface.
Quiz
At the first face of a glass prism, light travelling from air bends in which direction?
What is the angle between the incident direction produced and the emergent ray?
Why is the emergent ray through a rectangular slab parallel to the incident ray?
Which ray lies inside the prism?
At the second prism face, the ray usually travels from glass to air. How does it bend?
Practice Problems
- Define the angle of the prism. Answer: It is the angle between the two inclined lateral faces through which refraction occurs.
- Explain the two changes in direction as a ray passes through a prism. Answer: At entry from air to glass it bends towards the first normal. At exit from glass to air it bends away from the second normal.
- Distinguish the angle of emergence from the angle of deviation. Answer: The angle of emergence is measured between the emergent ray and the normal at the second face. The angle of deviation is measured between the incident direction produced and the emergent ray.
- A ray diagram shows the incident and emergent rays parallel after passing through a triangular prism. Identify the likely error. Answer: The diagram has treated the inclined prism faces like parallel slab faces. The two normals are differently directed, so a general prism ray should show net deviation.
- Describe how four pins can be used to trace refraction through a prism. Answer: Place two pins on the incident line. View their images through the second face and align two more pins with those images. Joining the pin positions after removing the prism reveals the incident and emergent paths; the entry and exit points are joined for the refracted path.
Key Takeaways
• A triangular prism has two triangular bases and three rectangular lateral surfaces. • Light bends towards the normal on entering glass and away from the normal on leaving it. • The incident, refracted and emergent rays occupy different parts of the complete path. • The angle of deviation compares the incident direction produced with the emergent ray. • A slab has parallel refracting faces, so its emergent ray is parallel but laterally displaced. • A prism has inclined refracting faces, so the emergent ray is generally deviated. • Angles of incidence, refraction and emergence must always be measured from the relevant normal.