Use simple constructions, measurements and calculations for reflection by plane mirrors

3.2.1 Reflection of Light

Learning Objective

Use simple constructions, measurements and calculations to investigate reflection by plane mirrors.

Syllabus Requirements (Cambridge IGCSE 0625 – 3.2.1)

• Define normal, angle of incidence (θ_i) and angle of reflection (θ_r).
• State the law of reflection: θ_i = θ_r.
• Describe the image formed by a plane mirror:
  • Virtual, upright, laterally inverted, same size as the object, and located the same distance behind the mirror as the object is in front.

Key Concepts

• The incident ray, reflected ray and the normal all lie in the same plane.
• Law of Reflection – the angle of incidence equals the angle of reflection (θ_i = θ_r).
• A plane mirror produces an image that is:
  • Virtual – cannot be projected on a screen.
  • Upright – same orientation as the object.
  • Laterally inverted – left–right reversed.
  • Same size as the object.
  • Located the same distance behind the mirror as the object is in front of it.

Definitions

Ray‑Diagram Construction (Plane Mirror)

1. Draw the mirror as a straight horizontal line.
2. Mark the point of incidence on the mirror.
3. Draw the normal at this point (perpendicular to the mirror).
4. From the object, draw the incident ray to the point of incidence.
5. Measure the angle between the incident ray and the normal – this is θ_i.
6. From the point of incidence draw the reflected ray on the opposite side of the normal such that θ_r = θ_i (use a protractor or set‑square).
7. Extend the reflected ray backwards as a dotted line. The intersection of this extension with the line drawn through the object parallel to the mirror gives the position of the virtual image.

Experimental Procedure & Measurements

For each trial record the quantities below. Use a ruler or measuring tape for distances and a protractor for angles.

Calculations

• Object–image distance relationship (plane mirror) \[ d_i = -\,d_o \] The negative sign indicates a virtual image located behind the mirror. This relationship follows directly from the law of reflection together with the similar‑triangle geometry of the ray diagram.
• Verification of the law of reflection \[ \Delta\theta = |\theta_i - \theta_r| \] A small Δθ (typically < 1°) confirms that the law holds within experimental uncertainty.

Law of Reflection (Command‑word “state”)

θ_i = θ_r

Example Problem

Given: An object is placed 30 cm in front of a plane mirror. The incident ray makes an angle of 35° with the normal.

Find:

1. The angle of reflection.
2. The position and nature of the image.

Solution:

1. By the law of reflection, θ_r = θ_i = 35°.
2. Using \(d_i = -d_o\): \[ d_i = -30\;\text{cm} \] The image is 30 cm behind the mirror. It is virtual, upright, laterally inverted, same size as the object, and cannot be captured on a screen.

Common Errors and How to Avoid Them

• Measuring angles from the mirror surface instead of the normal. Always draw the normal first and use it as the reference line.
• Confusing virtual and real images. A virtual image cannot be projected on a screen; it appears to be located behind the mirror.
• Incorrect sign convention for distances. In plane‑mirror calculations the image distance is taken as negative because the image lies on the opposite side of the reflecting surface.
• Overlooking lateral inversion. Remember that the image is left‑right reversed even though its size is unchanged.

Summary Checklist (AO2 – “State” & “Describe”)

• Normal, angle of incidence and angle of reflection are in the same plane.
• Law of reflection: θ_i = θ_r.
• Image formed by a plane mirror is:
  • Virtual
  • Upright
  • Laterally inverted
  • Same size as the object
  • Located the same distance behind the mirror as the object is in front of it.
• Quantitative relationship: \(d_i = -d_o\) (derived from similar triangles).
• Accurate ray‑diagram construction and careful measurement of angles verify the law of reflection.

Practice Questions

1. A student shines a laser beam at a plane mirror such that the incident angle is 20°. What is the angle of reflection?
2. An object is 45 cm in front of a plane mirror. Where is the image formed? State its nature (real/virtual, upright/inverted, size).
3. During an experiment the measured angles are θ_i = 40° and θ_r = 42°. Calculate Δθ and comment on the result.
4. Explain why a plane mirror does **not** change the size of the image, using the geometry of the ray diagram.
5. Is the image produced by a plane mirror laterally inverted? Justify your answer with reference to the ray diagram.