Reflection and Refraction Ray Diagrams
This topic covers the behaviour of light at surfaces. It explains how to predict the path of light rays using diagrams for both reflection (bouncing off a mirror) and refraction (bending through a new material), which are fundamental concepts in optics.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- The Law of Reflection states that the angle of incidence equals the angle of reflection. Both angles are always measured from the normal.i = r
- Plane mirrors form virtual images. The image is the same size as the object, the same distance behind the mirror as the object is in front, and is laterally inverted (left-to-right swapped).
- Refraction occurs when a wave, like light, changes speed as it crosses the boundary between two different media.
- If a wave slows down when entering a new medium (e.g., air to glass), it bends TOWARDS the normal.
- If a wave speeds up when entering a new medium (e.g., glass to air), it bends AWAY from the normal.
- A ray travelling along the normal (at 90 degrees to the surface) does not change direction, even though its speed changes.
Diagram
› Why does this happen?
Why do mirrors form 'virtual' images?
Your brain assumes light always travels in straight lines. When light rays from an object hit a mirror, they reflect. Your brain traces these reflected rays back in straight lines to a point where they appear to originate from. Because the light rays don't actually meet at this point behind the mirror — they just *appear* to — the image is called 'virtual'. You can't place a screen there to capture the image.
Why does changing speed cause light to bend?
Imagine a car driving from a smooth road (a 'fast' medium) into a muddy field (a 'slow' medium) at an angle. The wheel that hits the mud first slows down, while the other wheel continues at the faster road speed for a moment. This difference in speed across the axle forces the car to turn. Light behaves in a similar way. If a wave of light enters a new material at an angle, one side of it changes speed before the other. This causes the whole wave to pivot, changing its direction of travel. This bending is called refraction.
Formulae
i = r Used for all types of reflection from any surface, including plane and curved mirrors. It defines the direction of the reflected ray.
Definitions
- Normal
- An imaginary line drawn at a right angle (90°) to a surface at the point where a ray of light strikes it. It is the reference line for all optical angles.
- Angle of Incidence (i)
- The angle between the incoming ray of light and the normal.
- Angle of Reflection (r)
- The angle between the reflected ray of light and the normal.
- Angle of Refraction (r')
- The angle between the refracted ray of light (the ray that passes through the boundary) and the normal.
Worked example
A ray of light in air strikes the surface of a pond at an angle of incidence of 60°. The light travels slower in water than in air. The ray then reflects off a small flat mirror lying at the bottom of the pond. The mirror is parallel to the water's surface. What is the angle of reflection of the ray as it leaves the water surface to go back into the air?
- 1
Step 1:
The ray enters the water from the air.
Since it slows down, it bends TOWARDS the normal.
The angle of refraction will be less than 60°.
- 2
Step 2:
This refracted ray travels down to the mirror at the bottom.
Since the mirror is parallel to the surface, the normal to the mirror is parallel to the normal at the surface.
Therefore, the angle of incidence on the mirror is equal to the angle of refraction from Step 1.
- 3
Step 3:
The ray reflects off the mirror.
The law of reflection (i = r) applies.
The reflected ray leaves the mirror at the same angle it hit it.
- 4
Step 4:
This reflected ray now travels upwards to the water-air surface.
Due to the parallel geometry, its angle of incidence on the underside of the surface is the same as the angle of refraction from Step 1.
- 5
Step 5:
The ray now leaves the water and enters the air.
The path of light is reversible.
Since it entered at 60° and refracted to a smaller angle, it will now leave at that smaller angle and refract back to 60°.
The final angle of reflection from the pond surface (measured in the air) is 60°.
Answer: 60°
Common mistakes
- ×Measuring angles from the surface of the mirror or block, instead of from the normal. All angles (incidence, reflection, refraction) must be measured from the line perpendicular to the surface.
- ×Incorrectly applying the refraction rule. A common mistake is to bend the ray away from the normal when it slows down. Remember: Fast to Slow, moves Towards the normal (FST). Slow to Fast, moves Away from the normal (SFA).
- ×Assuming the angle of refraction is always smaller than the angle of incidence. This is only true when light slows down; the opposite occurs when light speeds up.
No-calculator tips
- ✓Always draw a large, clear ray diagram for any optics problem. Exaggerating the angles can help you visualise the correct direction of bending or reflection.
- ✓Draw the normal as a dotted line at every single boundary a ray crosses before you attempt to draw the next part of the ray's path.
- ✓For problems with multiple parallel surfaces (like a glass block in air), remember that the ray emerging will be parallel to the initial incident ray, just displaced sideways.