Solved Examples of the Law of Reflection: Algebra-Based

📚 Quick Study Guide

• 💡 The Law of Reflection states that the angle of incidence ($\theta_i$) is equal to the angle of reflection ($\theta_r$). Mathematically, this is expressed as: $\theta_i = \theta_r$.
• 📐 All angles are measured with respect to the normal, which is a line perpendicular to the reflecting surface at the point of incidence.
• 🔦 Incident ray: The ray of light approaching the reflecting surface.
• зеркало Reflected ray: The ray of light that bounces off the reflecting surface.
• 📏 Algebraic manipulations are often needed to solve for unknown angles when given related geometric information.
• ✨ Remember that the angles of incidence and reflection are *always* positive values.

🧪 Practice Quiz

1. What is the angle of reflection if the angle of incidence is 30 degrees?
   1. 15 degrees
   2. 30 degrees
   3. 60 degrees
   4. 90 degrees
2. A light ray strikes a mirror at an angle of 45 degrees to the normal. What is the angle between the incident ray and the reflected ray?
   1. 0 degrees
   2. 22.5 degrees
   3. 45 degrees
   4. 90 degrees
3. If the angle between the incident ray and the reflecting surface is 60 degrees, what is the angle of reflection?
   1. 30 degrees
   2. 60 degrees
   3. 90 degrees
   4. 120 degrees
4. A light ray is incident on a mirror. If the angle of reflection is 25 degrees, what is the angle between the reflected ray and the reflecting surface?
   1. 25 degrees
   2. 65 degrees
   3. 90 degrees
   4. 115 degrees
5. The angle of incidence is given by the expression $2x + 10$ degrees, and the angle of reflection is $x + 30$ degrees. What is the value of $x$?
   1. 10
   2. 20
   3. 30
   4. 40
6. A ray of light is reflected from a plane mirror. The angle between the incident ray and the mirror surface is $\theta$. What is the angle between the reflected ray and the mirror surface?
   1. $\theta$
   2. $2\theta$
   3. $90 - \theta$
   4. $180 - \theta$
7. A light ray hits a mirror at an angle of incidence of $x$. If the mirror is then rotated by 10 degrees, what is the change in the angle of reflection, assuming the incident ray remains fixed?
   1. 0 degrees
   2. 5 degrees
   3. 10 degrees
   4. 20 degrees