#AP Physics 2: Light - Reflection, Refraction, and Absorption 💡

Hey there, future AP Physics 2 master! Let's dive into the world of light and optics. This guide is designed to be your go-to resource, especially when you're cramming the night before the exam. We'll make sure everything is clear, concise, and memorable. Let's get started!

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Light Interactions: Reflection, Refraction, and Absorption

When light encounters a new medium, three things can happen:

• Reflection: Light bounces off the surface. Think of a mirror. 🪞
• Absorption: Light is converted into another form of energy, usually heat. This is why a black shirt gets hotter in the sun. 🔥
• Transmission: Light passes through the medium. Like light through a window. 🪟

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Reflection: Bouncing Back

• Specular Reflection: Occurs on smooth surfaces. The incoming light rays are reflected in an orderly way, preserving the image. Think of a mirror.

  

  Caption: Specular reflection on a smooth surface.

• Diffuse Reflection: Occurs on rough surfaces. Light rays are scattered in many directions. Think of a wall.

  

  Caption: Diffuse reflection on a rough surface.

#The Law of Reflection

When light reflects off a smooth surface:

• Incident Ray: The incoming light ray.
• Reflected Ray: The outgoing light ray.
• Normal Line: A line perpendicular to the surface at the point of incidence.
• Angle of Incidence (θi): The angle between the incident ray and the normal line.
• Angle of Reflection (θr): The angle between the reflected ray and the normal line.

Caption: Illustration of incident ray, reflected ray, and normal line.

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Refraction: Bending Light

Refraction is the bending of light as it passes from one medium to another. This happens because light changes speed when it enters a new medium.

• Refracted Ray: The ray that passes through into the new medium.
• Angle of Refraction (θ₂): The angle between the refracted ray and the normal line.

Caption: Illustration of refraction with incident and refracted rays.

• Light slows down: The light bends towards the normal (θ₂ < θ₁).
• Light speeds up: The light bends away from the normal (θ₂ > θ₁).

#Index of Refraction (n)

The index of refraction is a measure of how much light slows down in a medium. It's defined as:

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

Where:

• n is the index of refraction
• c is the speed of light in a vacuum (3.00 x 10⁸ m/s)
• v is the speed of light in the medium

Caption: Light refracts differently in different mediums due to varying refractive indices.

#Snell's Law

Snell's Law relates the angles of incidence and refraction to the indices of refraction of the two media:

$$n_1 \sin(θ_1) = n_2 \sin(θ_2)$$

Where:

• n₁ is the index of refraction of the incident medium.
• θ₁ is the angle of incidence.
• n₂ is the index of refraction of the refracting medium.
• θ₂ is the angle of refraction.

• If n₂ > n₁, then θ₂ < θ₁ (light bends towards the normal).
• If n₂ < n₁, then θ₂ > θ₁ (light bends away from the normal).

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Total Internal Reflection (TIR)

When light travels from a medium with a higher index of refraction to one with a lower index of refraction, it bends away from the normal. As the angle of incidence increases, the angle of refraction also increases. At a certain angle, the angle of refraction reaches 90 degrees. This is the critical angle (θc).

Caption: Illustration of critical angle and total internal reflection.

If the angle of incidence exceeds the critical angle, the light is completely reflected back into the original medium. This is called total internal reflection.

The critical angle can be calculated using:

$$sin(θ_c) = \frac{n_2}{n_1}$$

Where:

• n₁ is the index of refraction of the incident medium (higher n).
• n₂ is the index of refraction of the refracting medium (lower n).

#Final Exam Focus

Okay, you've made it through the key concepts! Here's what to focus on for the exam:

• Reflection: Understand specular vs. diffuse reflection and the law of reflection.
• Refraction: Master Snell's Law and the concept of the index of refraction. Know when light bends towards or away from the normal.
• Total Internal Reflection: Know the conditions for TIR and how to calculate the critical angle.
• Connections: Be prepared for questions that combine reflection, refraction, and TIR.

#Last-Minute Tips

• Time Management: Don't spend too long on a single question. If you're stuck, move on and come back later.
• Diagrams: Draw diagrams to visualize problems. It can make complex scenarios much clearer.
• Units: Double-check your units in calculations. A small error can cost you points.
• Practice: Do as many practice problems as you can. The more you practice, the more comfortable you'll be.
• Stay Calm: Take a deep breath. You've got this!

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Practice Question

Practice Problems

#Multiple Choice Questions

1. The critical angle of a material is the angle of incidence for which the angle of refraction is: A) 0° B) 30° C) 45° D) 90° E) 180°

2. A beam of light passes from medium 1 to medium 2 to medium 3 as shown in the figure. What is true about the respective indices of refraction (n₁, n₂, n₃)?

   

   A) n₁ > n₂ > n₃ B) n₁ > n₃ > n₂ C) n₂ > n₃ > n₁ D) n₂ > n₁ > n₃ E) n₃ > n₁ > n₂

3. A wave moves from one medium to a second medium with a different index of refraction. Which of the following wave properties would NEVER change? A) frequency B) wavelength C) speed D) angle E) all will change

#Free Response Question

A laser beam is incident on a prism with an index of refraction of 1.50 at an angle of 30 degrees as shown. The prism is surrounded by air (n=1.00). The laser beam then exits the prism into the air on the other side.

(a) Calculate the angle of refraction, θ₂, inside the prism. (b) Calculate the angle of incidence, θ₃, on the other side of the prism. (c) Calculate the angle of refraction, θ₄, when the laser beam exits the prism. (d) If the prism was submerged in water (n=1.33), how would the angle of refraction, θ₄, change? Explain your answer.

#FRQ Scoring Breakdown

(a) Calculate the angle of refraction, θ₂, inside the prism. (3 points)

• Use Snell's Law: n₁sinθ₁ = n₂sinθ₂
• (1.00)sin(30°) = (1.50)sinθ₂
• θ₂ = arcsin((1.00)sin(30°)/1.50) = 19.47°
  • 1 point for using Snell's Law.
  • 1 point for correct substitution.
  • 1 point for the correct answer.

(b) Calculate the angle of incidence, θ₃, on the other side of the prism. (2 points)

• The angle of incidence on the other side is equal to the angle of refraction on the first side due to the geometry of the prism. θ₃ = θ₂ = 19.47°
  • 1 point for recognizing the geometry.
  • 1 point for the correct answer.

(c) Calculate the angle of refraction, θ₄, when the laser beam exits the prism. (3 points)

• Use Snell's Law: n₁sinθ₃ = n₂sinθ₄
• (1.50)sin(19.47°) = (1.00)sinθ₄
• θ₄ = arcsin((1.50)sin(19.47°)/1.00) = 30° * 1 point for using Snell's Law. * 1 point for correct substitution. * 1 point for the correct answer.

(d) If the prism was submerged in water (n=1.33), how would the angle of refraction, θ₄, change? Explain your answer. (3 points)

• The angle of refraction, θ₄, would be smaller.
• When the prism is surrounded by water, the difference in refractive indices between the prism and the surrounding medium is smaller. This means the light will bend less when it exits the prism.
• Using Snell's Law, (1.50)sin(19.47°) = (1.33)sinθ₄, gives θ₄ = 22.08°
  • 1 point for stating that the angle is smaller.
  • 1 point for correct explanation.
  • 1 point for correct calculation.

#Answers to Multiple Choice Questions

1. D: Definition of critical angle.
2. D: More–Less dense bend away, Less–More dense bend towards. The more the bend, the bigger the difference in n’s.
3. A: Fact for refraction problems