### Solution
In this problem, we are given a set of angles of incidence and their corresponding measured angles of reflection. According to the law of reflection, the angle of incidence should equal the angle of reflection. We need to find the incorrectly measured angle of reflection and suggest what might have gone wrong.
#### Given Data:
| Angle of incidence | Angle of Reflection |
|---------------------|---------------------|
| [tex]$20^{\circ}$[/tex] | [tex]$20^{\circ}$[/tex] |
| [tex]$40^{\circ}$[/tex] | [tex]$39^{\circ}$[/tex] |
| [tex]$60^{\circ}$[/tex] | [tex]$30^{\circ}$[/tex] |
#### Part (a): Identifying the Incorrect Angle of Reflection
1. Compare each pair of angles:
- For an angle of incidence of [tex]$20^{\circ}$[/tex], the measured angle of reflection is [tex]$20^{\circ}$[/tex]. This follows the law of reflection.
- For an angle of incidence of [tex]$40^{\circ}$[/tex], the measured angle of reflection is [tex]$39^{\circ}$[/tex]. This does not follow the law of reflection; the reflection should also be [tex]$40^{\circ}$[/tex].
- For an angle of incidence of [tex]$60^{\circ}$[/tex], the measured angle of reflection is [tex]$30^{\circ}$[/tex]. This does not follow the law of reflection; the reflection should also be [tex]$60^{\circ}$[/tex].
2. Conclusion:
- The incorrect angles of reflection are [tex]$39^{\circ}$[/tex] (corresponding to an incident angle of [tex]$40^{\circ}$[/tex]) and [tex]$30^{\circ}$[/tex] (corresponding to an incident angle of [tex]$60^{\circ}$[/tex]).
Therefore, the angle of reflection measured incorrectly is [tex]$39^{\circ}$[/tex] for the angle of incidence [tex]$40^{\circ}$[/tex].
#### Part (b): Possible Errors
3. Analysis for [tex]$39^{\circ}$[/tex] angle of reflection:
- Human Error: The student may have read the protractor incorrectly or recorded the measurement inaccurately.
- Instrumental Error: The protractor or reflective surface might not have been perfectly positioned or aligned, leading to measurement errors.
4. General Observations:
- There might have been inconsistencies in the setup of the experiment.
- The angle of reflection not matching the angle of incidence suggests a potential procedural error or faulty equipment.
#### Conclusion:
- Incorrectly measured angle of reflection: [tex]$39^{\circ}$[/tex] (corresponding to the [tex]$40^{\circ}$[/tex] angle of incidence).
- Possible Explanation: The student might have read or recorded the angle incorrectly, suggesting either human error in reading/measuring or a possible experimental error.
