State that for reflection, the angle of incidence is equal to the angle of reflection; recall and use this relationship

Reflection of Light – Cambridge IGCSE Physics (0625) – 3.2.1

Learning Objective

State that for reflection the angle of incidence equals the angle of reflection; recall and use this relationship in calculations, constructions and simple image‑location problems.

Key Definitions

• Incident ray – the ray of light that strikes a surface.
• Reflected ray – the ray that leaves the surface after the incident ray strikes it.
• Normal – an imaginary line drawn perpendicular to the reflecting surface at the point of incidence.
• 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.
• Specular (mirror‑like) reflection – reflection from a smooth surface where parallel incident rays remain parallel after reflection.
• Diffuse reflection – reflection from a rough surface that scatters light in many directions; the law i = r does not apply.
• Plane mirror – a smooth, flat reflecting surface that produces specular reflection.
• Virtual image – an image formed where rays appear to diverge from a point behind the mirror; it cannot be projected onto a screen.

Law of Reflection

When a ray of light strikes a smooth (plane) surface, the angle it makes with the normal (the angle of incidence) is equal to the angle the reflected ray makes with the normal (the angle of reflection):

i = r

Both angles are measured on opposite sides of the normal.

Ray‑Diagram (sketch)

Construction Activity – Drawing a Reflection

1. Draw a straight line to represent the reflecting surface.
2. Mark a point P on the line – the point of incidence.
3. Using a ruler, draw the normal at P (perpendicular to the surface).
4. From a point above the surface draw the incident ray making a chosen angle i with the normal (measure with a protractor).
5. From P draw the reflected ray on the opposite side of the normal making the same angle r = i.
6. Extend the reflected ray backwards behind the mirror; the point where it appears to diverge is the virtual image I. Label it.
7. Measure both i and r with a protractor, record the values and calculate the percentage error:

   
   Percentage error = |r – i| ÷ i × 100 %.

   
   Comment on possible sources of error (e.g., parallax, ruler thickness, surface roughness).

Using the Law of Reflection

1. Identify the point of incidence on the reflecting surface.
2. Draw the normal at that point.
3. Read or measure the given angle of incidence i.
4. Apply the law i = r to obtain the angle of reflection.
5. Draw the reflected ray using the calculated angle.
6. Use the completed diagram to answer further questions (direction of reflected light, position of a virtual image, etc.).

Plane‑Mirror Image Characteristics

• The image is virtual – it cannot be projected onto a screen.
• The image is upright and the same size as the object.
• Object distance (OD) equals image distance (ID):

  \$\text{OD} = \text{ID}\$

  measured perpendicular to the mirror.

• The image is laterally inverted (left–right reversal).

Example 1 – Image Position

An object is placed 12 cm in front of a plane mirror. Where is the image formed?

Since OD = ID, the image is 12 cm behind the mirror, directly opposite the object. It is virtual, upright, same size, and laterally inverted.

Example 2 – Using OD = ID

An object is 25 cm from a plane mirror. A student measures the distance from the mirror to the apparent image and obtains 24 cm. Calculate the percentage error and suggest a reason for the discrepancy.

True image distance = 25 cm.

Error = |24 – 25| ÷ 25 × 100 % = 4 %.

Possible reasons: parallax when reading the image position, imperfect alignment of the ruler, or a slightly non‑planar mirror surface.

Real‑World Applications

• Periscope – two plane mirrors set at 45° reflect light from the top opening to the viewer’s eye, allowing observation over obstacles.
• Rear‑view (road) mirrors – the law of reflection explains why the driver sees a virtual image of traffic behind the vehicle.
• Household mirrors – give the familiar virtual image that appears to be behind the glass.

Common Misconceptions

• Measuring angles from the surface instead of from the normal.
• Assuming the law applies to rough surfaces; it only holds for smooth (specular) reflections.
• Thinking the incident and reflected rays lie on the same side of the normal.
• Believing the image formed by a plane mirror is real or located on the mirror surface; it is virtual and cannot be projected.

Worked Example

Question: A ray of light strikes a plane mirror at an angle of incidence of \$30^\circ\$. What is the angle of reflection? If the incident ray makes an angle of \$45^\circ\$ with the mirror surface, find the angle of incidence and the angle of reflection.

Solution:

1. Given \$i = 30^\circ\$, by the law of reflection \$r = i = 30^\circ\$.
2. The angle between the incident ray and the mirror surface is the complement of the angle of incidence:

   \$i = 90^\circ - 45^\circ = 45^\circ.\$

   Hence \$r = i = 45^\circ\$.

Practice Questions

1. A light ray strikes a flat mirror at an angle of incidence of \$22^\circ\$. Determine the angle of reflection.
2. If the angle between the incident ray and the mirror surface is \$70^\circ\$, find the angle of incidence and the angle of reflection.
3. In a diagram the normal to a plane mirror makes a \$15^\circ\$ angle with the reflected ray. What is the angle of incidence?
4. An object is 18 cm in front of a plane mirror. State the position, size and nature (real/virtual) of the image.
5. Explain, using the law of reflection, why a periscope allows a person to see over a wall.
6. Measurement‑validation task: Draw a ray diagram where \$i = 35^\circ\$. Measure \$r\$ and calculate the percentage error. List at least two possible sources of error.
7. OD = ID problem: An object is 30 cm from a plane mirror. A student measures the distance from the mirror to the apparent image as 28 cm. Calculate the percentage error and suggest why the measurement differs from the expected value.

Summary Table

Key Take‑away

For any smooth reflecting surface the angle of incidence equals the angle of reflection (i = r). This simple relationship lets you construct reflected rays, locate virtual images formed by plane mirrors, evaluate experimental accuracy, and explain everyday devices such as periscopes and rear‑view mirrors.