Angles of Reflection

What you’ll learn

Measure light angles from the normal to a mirror.

វាស់មុំពន្លឺធៀបនឹងបន្ទាត់កែងនឹងកញ្ចក់។

Meaning and use

For a smooth plane mirror, the angle of incidence equals the angle of reflection. Both are measured from the normal, the line perpendicular to the surface. The incident ray, reflected ray, and normal lie in one plane. An angle measured from the mirror surface needs conversion first.

ក្នុងការឆ្លុះលើកញ្ចក់រាប មុំចំណាំងផ្លាតស្មើមុំចំណាំងចូល ដោយវាស់ពីបន្ទាត់ណរម៉ាល់។ បន្ទាត់នេះកែងនឹងផ្ទៃកញ្ចក់។

Formulas

Law of reflection

\[\theta_i=\theta_r\]

Surface-to-normal conversion

\[\theta_{\mathrm{normal}}=90^\circ-\theta_{\mathrm{surface}}\]

Symbols and units

Symbol	Meaning	Unit or restriction
θi	Angle of incidence measured from the normal	Degrees
θr	Angle of reflection measured from the normal	Degrees
Normal	Line perpendicular to the reflecting surface	Reference direction

Conditions and limits

• Use the normal, not the surface, as the angle reference.
• Examples assume reflection at a smooth plane surface.
• មុំត្រូវមានចំណុចយោងដូចគ្នាមុនប្រៀបធៀប។

Worked examples

Angle from the normal

A ray strikes at 35° to the normal.

1. Apply \(\theta_r=\theta_i\).
2. Therefore \(\theta_r=35^\circ\).

35° from the normal

មុំចូល និងមុំឆ្លុះវាស់ពីណរម៉ាល់ដូចគ្នា។

Angle from the surface

The incident ray is 20° to the mirror surface.

1. Incidence from normal \(90^\circ-20^\circ=70^\circ\).
2. Reflection from normal is also 70°.

70° from the normal

ត្រូវដកពី 90 ដឺក្រេមុនប្រើច្បាប់ឆ្លុះ។

Common mistakes

Instead of	Use	Why
A ray 20° to the mirror has incidence angle 20°.	Its incidence angle from the normal is 70°.	Surface and normal references are complementary.
Reflection angle is measured from a different normal.	Use the same normal at the reflection point.	The law compares like reference angles.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Incidence is 50° from the normal. Find reflection angle.
2. A ray is 30° to the surface. Find incidence angle.
3. A ray arrives along the normal. What are its incidence and reflection angles?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 50°

   The angles are equal.

2. 60°

   90 − 30 = 60.

3. Both are 0°.

   The ray retraces its path in this ideal plane-mirror case.

Quick recap

• Draw the normal first.
• Compare angles measured from the normal.
• Convert a surface angle using 90° minus that angle.