Reflection of light

1. Overview

Reflection occurs when light bounces off a surface. This phenomenon allows us to see non-luminous objects and is the fundamental principle behind mirrors, periscopes, and many optical instruments. Understanding how light reflects allows us to predict where images will appear and how they will look.

Key Definitions

• Normal: An imaginary line drawn perpendicular (at 90°) to the reflecting surface at the point where the light ray strikes.
• Incident Ray: The incoming ray of light that strikes the surface.
• Reflected Ray: The ray of light that bounces off the surface.
• Angle of Incidence ($i$): The angle between the incident ray and the normal.
• Angle of Reflection ($r$): The angle between the reflected ray and the normal.
• Virtual Image: An image formed by light rays that appear to diverge from a point, but do not actually pass through it. It cannot be projected onto a screen.
• Lateral Inversion: The reversal of an image where the left side appears as the right side and vice versa.

Core Content

The Law of Reflection

For any smooth, reflecting surface, the following rule always applies: The angle of incidence is equal to the angle of reflection ($i = r$).

Characteristics of an Image in a Plane Mirror

The image formed by a plane (flat) mirror has five specific characteristics:

1. Same Size: The image is exactly the same height and width as the object.
2. Same Distance: The image is the same distance behind the mirror as the object is in front of it.
3. Virtual: The light rays do not actually meet behind the mirror; your brain "traces" them back.
4. Upright: The image is not upside down.
5. Laterally Inverted: The left and right sides are swapped (e.g., if you raise your right hand, the image raises its left).

Ray Diagrams

When drawing reflection:

• Always use a ruler and sharp pencil.
• Always draw the normal as a dotted line first.
• Ensure the rays have arrows showing the direction of light travel.

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Extended Content (Extended Curriculum Only)

Using Construction for Reflection

To locate an image accurately in a mirror, you should follow these steps:

1. Draw a line from the object perpendicular to the mirror.
2. Measure the distance from the object to the mirror and mark the image point at the exact same distance behind the mirror.
3. Draw a reflected ray from the mirror to the eye.
4. Use a dotted line to connect the reflected ray back to the virtual image point.

Worked Example: Distance Calculation

Question: An object is placed 1.5 meters in front of a plane mirror. How far is the object from its image? Solution:

• Distance from object to mirror = 1.5m.
• Distance from mirror to image = 1.5m.
• Total distance = $1.5\text{m} + 1.5\text{m} = 3.0\text{m}$.

Field of View

An observer can only see an object in a mirror if a light ray can travel from the object, hit the mirror, and reflect into the observer’s eye. If the mirror is too short or the object is too far to the side, the light will miss the mirror, and the object will not be visible.

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Key Equations

• The Law of Reflection: $i = r$
  • $i$: Angle of incidence (measured in degrees, °)
  • $r$: Angle of reflection (measured in degrees, °)
• Image Distance: $d_{o} = d_{i}$
  • $d_{o}$: distance of object from mirror (m)
  • $d_{i}$: distance of image from mirror (m)

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Common Mistakes to Avoid

• ❌ Wrong: Measuring the angle between the light ray and the mirror surface.
• ✓ Right: Always measure the angle between the light ray and the normal. (The angles against the mirror are called "glancing angles" and are not used in the law of reflection).
• ❌ Wrong: Thinking all letters change appearance in a mirror.
• ✓ Right: Symmetrical letters like 'A', 'H', or 'i' (if drawn as a simple stroke) look the same because their lateral inversion is identical to their original shape.
• ❌ Wrong: Labeling the image as "real" because you can see it.
• ✓ Right: Mirror images are always virtual because light rays do not actually pass through the mirror to the image point.
• ❌ Wrong: Confusing the normal with a light ray.
• ✓ Right: The normal is a reference line only; light does not "travel" along it unless the incident ray is at 0°.

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Exam Tips

1. Precision matters: If a question asks you to complete a ray diagram, use a protractor to ensure $i = r$. Examiners allow a very small margin of error (usually ±1° or 2°).
2. Object-Image Alignment: Always ensure the line connecting the object and the image is perpendicular (90°) to the mirror. If the object is at an angle, the image must be reflected at that same angle relative to the mirror's plane.
3. Clock Problems: If an exam asks for the time on a reflected clock, remember to "flip" the entire face. A hand pointing at '3' will appear to point at '9' in the reflection.

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

A student sets up a plane mirror to investigate the reflection of light.

(a) Define the term 'angle of incidence' in the context of reflection. [2]

(b) State the law of reflection. [1]

(c) The student shines a ray of light at the mirror with an angle of incidence of 40°. Determine the angle between the incident ray and the reflected ray. [2]

Worked Solution:

(a)

1. The angle of incidence is the angle between the incident ray and the normal. [Definition of angle of incidence]
2. The normal is an imaginary line perpendicular to the surface at the point of incidence. [Definition of the normal]

How to earn full marks:

• Correctly define the angle of incidence, including reference to the normal (1 mark)
• Correctly define the normal (1 mark)

(b)

1. The angle of incidence is equal to the angle of reflection. [Statement of the law of reflection]

How to earn full marks:

• State that the angle of incidence equals the angle of reflection (1 mark)

(c)

1. The angle of reflection is equal to the angle of incidence, which is 40°. [Applying the law of reflection]
2. The angle between the incident and reflected ray is $40° + 40° = 80°$. [Calculating the total angle]

How to earn full marks:

• State or imply the angle of reflection is 40° (1 mark)
• Correctly calculate the total angle and give the correct units: $\boxed{80°}$ (1 mark)

Common Pitfall: Many students forget that the angle between the incident and reflected ray is the sum of the angle of incidence and the angle of reflection. Also, remember that the normal is a construction line, not the path of light.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

A small toy car is placed 25 cm in front of a plane mirror.

(a) Describe three characteristics of the image formed by the plane mirror. [3]

(b) The toy car is now moved to a distance of 40 cm in front of the mirror. State what happens to:

(i) the distance of the image from the mirror. [1]

(ii) the size of the image. [1]

(c) Give one everyday example of the use of a plane mirror. [1]

Worked Solution:

(a)

1. The image is the same size as the object. [Characteristic 1: Image size]
2. The image is the same distance behind the mirror as the object is in front. [Characteristic 2: Image distance]
3. The image is virtual. [Characteristic 3: Image type]

How to earn full marks:

• State each correct characteristic clearly. (1 mark per characteristic)

(b) (i)

1. The distance of the image from the mirror increases. It will be 40 cm behind the mirror. [Effect on image distance]

How to earn full marks:

• State that the image distance increases, or give the new image distance (1 mark)

(ii)

1. The size of the image remains the same. [Effect on image size]

How to earn full marks:

• State that the image size remains the same (1 mark)

(c)

1. Examples include: looking at yourself in a bathroom mirror, rear-view mirrors in cars, periscopes. [Use of a plane mirror]

How to earn full marks:

• Give a valid example of the use of a plane mirror (1 mark)

Common Pitfall: Students often confuse real and virtual images. Remember that a virtual image cannot be projected onto a screen, and it's formed by the apparent intersection of light rays. Also, the image in a plane mirror is always the same size as the object, regardless of the distance.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A student is investigating the reflection and refraction of light using a rectangular glass block and a ray box. The student shines a ray of light at an angle onto one side of the block.

(a)

Draw a diagram to show the path of the ray of light as it enters, travels through, and exits the glass block. Include the normal at each surface where refraction occurs. [4]

(b) The student measures the angle of incidence $i$ and the angle of refraction $r$ at the first surface. The following data is collected: $i = 60°$, $r = 35°$.

(i) Calculate the refractive index $n$ of the glass. [2]

(ii) State what happens to the speed of light as it enters the glass block. [1]

(iii) Suggest one reason why the emergent ray is parallel to the incident ray. [1]

Worked Solution:

(a)

How to earn full marks:

• Ray refracts towards the normal on entering the block (1 mark)
• Ray travels in a straight line through the block (1 mark)
• Ray refracts away from the normal on exiting the block (1 mark)
• Emergent ray is parallel to incident ray and normals are drawn at the point of incidence at both surfaces (1 mark)

(b) (i)

1. The refractive index is given by $n = \frac{\sin i}{\sin r}$. [Stating the formula for refractive index]
2. $n = \frac{\sin 60°}{\sin 35°} = \frac{0.866}{0.574} = 1.51$. [Substituting values and calculating]

How to earn full marks:

• Correctly substitute the given values into the correct formula (1 mark)
• Correct answer with no units: $\boxed{1.51}$ (1 mark)

(ii)

1. The speed of light decreases as it enters the glass block. [Speed of light in a denser medium]

How to earn full marks:

• State the speed of light decreases (1 mark)

(iii)

1. The sides of the glass block are parallel. [Reason for parallel rays]

How to earn full marks:

• State that the sides of the block are parallel (1 mark)

Common Pitfall: When drawing ray diagrams, many students don't accurately show the refraction at each surface. Remember that light bends towards the normal when entering a denser medium (like glass) and away from the normal when exiting. Also, be sure to use the correct formula for refractive index: $n = \frac{\sin i}{\sin r}$.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A student is setting up an experiment to investigate the reflection of light from a plane mirror. The apparatus includes a ray box, a plane mirror, a protractor, a ruler, and a piece of paper.

(a) Describe a method the student could use to accurately determine the angle of incidence and the angle of reflection. Your description should include:

(i) how to set up the apparatus. [2]

(ii) how to ensure accurate measurements. [3]

(b) The student performs the experiment and obtains the following data:

Angle of Incidence ($i$)	Angle of Reflection ($r$)
25°	26°
35°	36°
45°	46°
55°	56°

(i) State whether the data supports the law of reflection. Justify your answer. [2]

(ii) Suggest two possible sources of error in this experiment. [2]

Worked Solution:

(a) (i)

1. Place the plane mirror vertically on the piece of paper, using a ruler to ensure it's straight. [Positioning the mirror]
2. Shine a ray of light from the ray box towards the mirror at an angle. [Creating the incident ray]

How to earn full marks:

• Correctly describe how to position the mirror, mentioning a ruler for accuracy (1 mark)
• Correctly describe how to create the incident ray (1 mark)

(ii)

1. Mark two points along the incident and reflected rays on the paper, as far apart as possible, and then draw a line connecting the points to represent the rays. [Marking the rays]
2. Remove the mirror and use a ruler to draw the normal to the mirror surface at the point where the incident ray hits the mirror, ensuring it is perpendicular. [Drawing the normal]
3. Use a protractor to measure the angle of incidence and the angle of reflection, ensuring the protractor is aligned correctly with the normal and reading the scale at eye level to avoid parallax error. [Measuring the angles]

How to earn full marks:

• Describe how to accurately mark the incident and reflected rays using two points (1 mark)
• Describe how to draw an accurate normal using a ruler (1 mark)
• Describe how to accurately measure the angles using a protractor and avoiding parallax error (1 mark)

(b) (i)

1. The data supports the law of reflection. [Statement]
2. The angle of reflection is approximately equal to the angle of incidence in each case. The differences are small (around 1 degree) and likely due to experimental error. [Justification]

How to earn full marks:

• State that the data supports the law of reflection (1 mark)
• Justify the answer by stating that the angles are approximately equal and the differences are likely due to error, quoting the approximate error (1 mark)

(ii)

1. Parallax error when reading the protractor scale. [Error 1]
2. The width of the light ray makes it difficult to accurately mark the path of the ray. [Error 2]

How to earn full marks:

• Suggest each valid error clearly (1 mark per error)

Common Pitfall: When describing experimental methods, be specific about how to improve accuracy. For example, marking two points far apart on the ray helps to draw a more accurate line. Also, always consider parallax error when reading scales on instruments like protractors.