Reflection and Refraction - Physics Q and A

« Back to AP Physics Guide / Unit 13: Geometric Optics / 13.1 & 13.3: Reflection & Refraction

$A glowing laser beam hitting a glass prism, showing both a reflected beam and a bent refracted beam inside the glass.$

Geometric Optics: Visualizing how light travels and interacts with boundaries between different mediums.

When a light wave traveling through a medium encounters a boundary with a new medium (like light going from air into water), part of the wave bounces back into the original medium (Reflection), and part of it transmits into the new medium, changing speed and direction (Refraction).

1. The Law of Reflection (Topic 13.1)

Reflection is the bouncing of light off a surface. In geometric optics, we always measure angles relative to the normal line—an imaginary line drawn perpendicular to the surface boundary.

$\theta_i = \theta_r$

The angle of incidence ( $\theta_i$ ) equals the angle of reflection ( $\theta_r$ ).

Diagram showing an incident ray and a reflected ray striking a flat mirror, with both angles equal relative to a dashed normal line.

Specular Reflection: Light reflecting off a smooth surface keeps parallel rays parallel.

Concept First: Always measure your angles from the Normal (perpendicular to the surface), not from the surface itself! A common trick on the AP exam is to give you the angle between the ray and the surface.

2. Index of Refraction ( $n$ )

Light travels fastest in a vacuum ( $c \approx 3 \times 10^8 \text{ m/s}$ ). When it enters a physical medium (like water or glass), it slows down. The index of refraction ( $n$ ) is a ratio that tells us how much the medium slows down the light.

$n = \frac{c}{v}$

Where $c$ is the speed of light in a vacuum, and $v$ is the speed of light in the medium. Because $v$ can never exceed $c$ , $n \ge 1$ always.

3. Refraction & Snell’s Law (Topic 13.3)

Because light changes speed when it enters a new medium at an angle, the light ray bends. This bending is called refraction. The relationship between the angles and the indices of refraction is given by Snell’s Law.

$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$

Where $n_1$ and $\theta_1$ are the index and angle of the incident medium, and $n_2$ and $\theta_2$ belong to the refracting medium.

If light travels from a fast medium to a slow medium ( $n_1 < n_2$ ), it bends towards the normal.
If light travels from a slow medium to a fast medium ( $n_1 > n_2$ ), it bends away from the normal.

⚙️ Interactive Snell’s Law Simulator

Adjust the incident angle and the indices of refraction ( $n$ ) to see how light bends across the boundary.

Incident Angle ( $\theta_1$ ): 45°

Medium 1 ( $n_1$ ): 1.0

Medium 2 ( $n_2$ ): 1.5

Refracted Angle ( $\theta_2$ ): 28.1°

4. Total Internal Reflection (TIR)

As you may have seen in the simulator above, if light travels from a slow medium to a fast medium (like water to air), it bends away from the normal. If the incident angle is large enough, the refracted angle will hit 90° and run parallel to the boundary. The angle where this happens is the Critical Angle ( $\theta_c$ ).

If the incident angle is greater than the critical angle ( $\theta_1 > \theta_c$ ), the light cannot escape the medium. It reflects entirely back inside. This is Total Internal Reflection, and it is how fiber optic cables work!

$\sin(\theta_c) = \frac{n_2}{n_1}$

This formula only works when $n_1 > n_2$ . (You cannot take the inverse sine of a number greater than 1).

5. Quick AP Practice

📚 Unit 13.1 & 13.3 Mastery Challenge

1. A light ray traveling in air ( $n=1.0$ ) strikes a glass block ( $n=1.5$ ) at an angle of 30° relative to the surface of the glass. What is the angle of refraction?

Check Answer

Trap Alert! The angle relative to the surface is 30°, which means the angle of incidence (relative to the normal) is $\theta_1 = 90^\circ - 30^\circ = 60^\circ$ .

Apply Snell’s Law: $(1.0)\sin(60^\circ) = (1.5)\sin(\theta_2)$
$\sin(\theta_2) = \frac{0.866}{1.5} = 0.577$
$\theta_2 = 35.3^\circ$

2. Can Total Internal Reflection occur when light travels from air ( $n=1.0$ ) into water ( $n=1.33$ )?