Waves & Electromagnetic Radiation

Physics: HS-PS4

An NGSS-aligned unit covering wave properties, the electromagnetic spectrum, wave–particle models, classical optics, digital information, and the technologies that put wave science to work. Each section is tagged with the NGSS Performance Expectation(s), Science & Engineering Practice(s), Disciplinary Core Idea(s), and Crosscutting Concept(s) it addresses.

NGSS Standards Wave Fundamentals EM Spectrum Wave vs. Particle Reflection Refraction Snell’s Law Total Internal Reflection Mirrors Lenses Polarization Digital Information Wave Technology Da Vinci Project

NGSS Performance Expectations

This unit addresses the Next Generation Science Standards topic HS-PS4: Waves and Electromagnetic Radiation. Every section below maps to at least one Performance Expectation, Science & Engineering Practice, Disciplinary Core Idea, and Crosscutting Concept.

HS-PS4-1 Wave Speed, Frequency & Wavelength

Use mathematical representations to support a claim about the relationship among the frequency, wavelength, and speed of waves traveling in various media.

HS-PS4-2 Digital Information

Evaluate questions about the advantages of using digital transmission and storage of information.

HS-PS4-3 Wave & Particle Models

Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other.

HS-PS4-4 Radiation & Matter

Evaluate the validity and reliability of claims in published materials about the effects that different frequencies of electromagnetic radiation have when absorbed by matter.

HS-PS4-5 Wave Technology

Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy.

Science & Engineering Practices

SEP Using Mathematics and Computational Thinking
SEP Asking Questions and Defining Problems
SEP Engaging in Argument from Evidence
SEP Obtaining, Evaluating, and Communicating Information

Disciplinary Core Ideas

PS4.A Wave Properties
PS4.B Electromagnetic Radiation
PS4.C Information Technologies and Instrumentation
PS3.D Energy in Chemical Processes (solar cells)

Crosscutting Concepts

CCC Cause and Effect
CCC Systems and System Models
CCC Stability and Change

1. Wave Fundamentals

HS-PS4-1 Using Math PS4.A Cause & Effect

A wave is a disturbance that transfers energy without transferring matter. All waves—whether on a string, in air, or through the vacuum of space—share a common mathematical relationship linking speed, frequency, and wavelength.

v = f λ c = 3.00 × 10⁸ m/s (speed of light in vacuum)

Wavelength (λ)

The distance between successive identical points on a wave (crest to crest or trough to trough). Measured in meters.

Frequency (f)

The number of complete wave cycles that pass a point each second. Measured in hertz (Hz). Period T = 1/f.

Wave Speed (v)

How fast the wave disturbance propagates through the medium. Depends on the medium’s properties, not the wave source.

When a wave enters a new medium, its speed changes, but its frequency stays the same (frequency is set by the source). Because v = fλ, the wavelength must change to compensate. This is why light bends at a boundary—one side of the wavefront slows down before the other.

Problem 1: A radio station broadcasts at a frequency of 98.5 MHz. What is the wavelength of these electromagnetic waves?

Show solution

λ = c / f = (3.00 × 10⁸ m/s) / (98.5 × 10⁶ Hz) = 3.05 m.

Problem 2: Green light has a wavelength of about 530 nm in vacuum. What is its frequency?

Show solution

f = c / λ = (3.00 × 10⁸) / (530 × 10⁻⁹) = 5.66 × 10¹⁴ Hz.

Problem 3: Sound travels at 343 m/s in air. A tuning fork vibrates at 440 Hz. What is the wavelength of the sound wave?

Show solution

λ = v / f = 343 / 440 = 0.780 m.

Problem 4: Light enters glass (n = 1.50) from vacuum. If the wavelength in vacuum is 600 nm, what is the wavelength inside the glass?

Show solution

In glass, v = c/n. Frequency is unchanged, so λ_glass = λ_vacuum/n = 600 nm / 1.50 = 400 nm. The wavelength shortens because the wave slows down.

2. The Electromagnetic Spectrum

HS-PS4-4 Evaluating Information PS4.B Cause & Effect

Electromagnetic waves span an enormous range of frequencies and wavelengths, but they all travel at the speed of light in vacuum. The energy carried by each photon depends on the frequency: E = hf, where h = 6.63 × 10⁻³⁴ J·s is Planck’s constant. Higher frequency means higher photon energy, which determines how radiation interacts with matter.

Radio

Microwave

Infrared

Visible

Ultraviolet

X-ray

Gamma

Low frequency / long wavelength / low photon energy ← → High frequency / short wavelength / high photon energy

Low-Energy Radiation

Radio waves, microwaves, and infrared radiation have relatively low photon energies. When absorbed, they increase molecular motion—heat. Infrared and visible light are converted to thermal energy in matter. This is why sunlight warms your skin.

High-Energy Radiation

Ultraviolet, X-rays, and gamma rays have enough energy per photon to ionize atoms—they knock electrons free. Ionizing radiation can damage DNA and living tissue. This is why excessive UV exposure causes sunburn and increases cancer risk.

Problem 1: Calculate the photon energy for red light (f = 4.3 × 10¹⁴ Hz) and for an X-ray (f = 3.0 × 10¹⁸ Hz). Why is the X-ray more dangerous to tissue?

Show solution

E_red = hf = (6.63 × 10⁻³⁴)(4.3 × 10¹⁴) = 2.85 × 10⁻¹⁹ J. E_X-ray = (6.63 × 10⁻³⁴)(3.0 × 10¹⁸) = 1.99 × 10⁻¹⁵ J. The X-ray photon carries about 7,000 times more energy. That is enough energy to ionize atoms, which can break chemical bonds in DNA and damage living tissue. Red light photons can only raise electrons to low-energy excited states; they cannot ionize atoms.

Claim Evaluation: A product advertisement claims that “5G radio signals at 28 GHz cause cellular damage because they have high frequency.” Evaluate this claim using what you know about photon energy and ionization.

Show solution

E = hf = (6.63 × 10⁻³⁴)(28 × 10⁹) = 1.86 × 10⁻²³ J. This is about 10,000 times less energy than a single photon of visible light and millions of times less than the energy needed to ionize atoms or break molecular bonds. The claim that “high frequency” 5G radio signals cause cellular damage is not supported by the physics of photon energy. Ionization requires UV frequencies or higher, which are many orders of magnitude above radio frequencies.

3. Wave and Particle Models of Light

HS-PS4-3 Argument from Evidence PS4.B Systems & Models

Electromagnetic radiation can be described by two complementary models. The wave model explains phenomena like interference and diffraction. The particle (photon) model explains phenomena like the photoelectric effect. For any given situation, one model typically provides a clearer explanation than the other.

Interference

When two waves overlap, they add constructively (bright spots) or destructively (dark spots) depending on their relative phase. This is best explained by the wave model. Waves can add or cancel when they meet, but then continue through each other unaffected.

Diffraction

When waves pass through a narrow slit or around an obstacle, they spread and bend into the shadowed region. Narrower slits produce wider diffraction patterns. The wave model predicts this spreading; a particle model cannot.

Photoelectric Effect

When light strikes a metal surface, electrons are emitted only if the light frequency exceeds a threshold. Increasing brightness (more photons) produces more electrons but does not change their energy. The particle (photon) model explains this; the wave model cannot.

Argument Task: A student observes a laser beam passing through a narrow slit and forming a wide band of light on a distant screen, rather than a narrow bright line. Which model—wave or particle—better explains this observation? Construct an argument using evidence and reasoning.

Show solution

Claim: The wave model better explains this observation. Evidence: The light spread out after passing through the slit, producing a central bright band wider than the slit, with dimmer bands on either side. Reasoning: Diffraction occurs when a wave encounters an opening comparable in size to its wavelength. The wave bends around the edges of the slit and spreads into the region beyond. A particle model would predict a narrow bright line matching the slit width, with sharp shadows—not the broad pattern observed.

Argument Task: An experiment shows that violet light ejects electrons from a metal plate, but red light of any intensity does not. Which model better explains this? Justify your answer.

Show solution

Claim: The particle (photon) model better explains this observation. Evidence: Violet light (higher frequency) ejects electrons; red light (lower frequency) does not, regardless of intensity. Reasoning: In the photon model, each photon carries energy E = hf. Violet photons have enough energy individually to overcome the metal’s work function and free an electron. Red photons, each carrying less energy, cannot free electrons no matter how many arrive. The wave model incorrectly predicts that increasing intensity (energy per time) should eventually eject electrons regardless of frequency.

4. Reflection

HS-PS4-1 PS4.A Cause & Effect

Reflection occurs when light bounces from a surface. Angles are measured from the normal line, not from the surface.

Law of Reflection: θ_i = θ_r

Problem 1: A light ray strikes a plane mirror at an angle of 32° from the normal. What is the angle of reflection?

Show solution

The angle of reflection equals the angle of incidence, so θ_r = 32°.

Problem 2: A ray makes a 65° angle with the mirror surface. What angle does the reflected ray make with the normal?

Show solution

Angles in reflection are measured from the normal. The normal is 90° from the surface, so θ_i = 90° − 65° = 25°. Therefore θ_r = 25°.

5. Refraction

HS-PS4-1 Using Math PS4.A Cause & Effect

Refraction is the bending of light as it changes speed when moving from one medium into another. Light bends toward the normal when it enters a slower, higher-index medium and away from the normal when it enters a faster, lower-index medium. The index of refraction relates the speed of light in a medium to its speed in vacuum.

Index of refraction: n = c / v

Problem 1: Light travels through a material at 2.00 × 10⁸ m/s. What is the index of refraction?

Show solution

n = c/v = (3.00 × 10⁸)/(2.00 × 10⁸) = 1.50.

Problem 2: A ray enters glass from air. In your diagram, should it bend toward or away from the normal?

Show solution

Glass has a larger index of refraction than air, so the ray slows down and bends toward the normal.

6. Snell’s Law

HS-PS4-1 Using Math PS4.A Cause & Effect

Snell’s Law quantifies refraction. It connects the angle in the first medium to the angle in the second medium using the wave speed relationship v = fλ and the index of refraction.

n₁ sin(θ₁) = n₂ sin(θ₂)

Angles are always measured from the normal.

Problem 1: Light travels from air (n = 1.00) into water (n = 1.33) at θ₁ = 40°. Find θ₂.

Show solution

1.00 sin(40°) = 1.33 sin(θ₂). So sin(θ₂) = 0.6428/1.33 = 0.483. θ₂ ≈ 28.9°.

Problem 2: Light travels from glass (n = 1.50) into air (n = 1.00) at θ₁ = 30°. Find θ₂.

Show solution

1.50 sin(30°) = 1.00 sin(θ₂). sin(θ₂) = 0.750. θ₂ ≈ 48.6°.

7. Total Internal Reflection

HS-PS4-1 HS-PS4-5 Using Math PS4.A PS4.C Cause & Effect

When light passes from a higher-index medium (like glass or water) into a lower-index medium (like air), it bends away from the normal. As the angle of incidence increases, the refracted ray bends further from the normal. At the critical angle, the refracted ray skims along the boundary at 90°. Beyond that angle, no light crosses the boundary—it reflects entirely back into the denser medium. This is total internal reflection (TIR).

Critical angle: sin(θ_c) = n₂ / n₁ (requires n₁ > n₂)

Derived from Snell’s Law by setting θ₂ = 90°: n₁ sin(θ_c) = n₂ sin(90°) = n₂.

Applications: Fiber Optics

Total internal reflection is the principle behind fiber optic cables. Light enters one end of a thin glass or plastic fiber and bounces along at angles greater than the critical angle, trapped inside the core. Because each reflection is total, the signal travels long distances with very little loss. Fiber optics are the backbone of modern digital communication, carrying internet data as pulses of light.

Applications: Diamonds

Diamond has one of the highest indices of refraction (n = 2.42), giving it a very small critical angle of about 24.4°. Most light entering a well-cut diamond hits the internal facets at angles above the critical angle, trapping and redirecting the light before it exits through the top. This is what creates a diamond’s signature brilliance and sparkle.

Problem 1: Find the critical angle for light traveling from diamond (n = 2.42) into air (n = 1.00).

Show solution

sin(θ_c) = n₂/n₁ = 1.00/2.42 = 0.413. θ_c = sin⁻¹(0.413) ≈ 24.4°. Any light hitting a diamond-air boundary at more than 24.4° from the normal undergoes total internal reflection.

Problem 2: Find the critical angle for light traveling from water (n = 1.33) into air (n = 1.00).

Show solution

sin(θ_c) = 1.00/1.33 = 0.752. θ_c = sin⁻¹(0.752) ≈ 48.8°. A swimmer looking up from underwater sees the world compressed into a bright circle directly overhead; outside that circle, the water surface acts as a mirror due to TIR.

Problem 3: Light inside a plastic rod (n = 1.62) strikes the plastic-air boundary at 54° from the normal. Does the light exit the rod or undergo total internal reflection?

Show solution

First find the critical angle: sin(θ_c) = 1.00/1.62 = 0.617. θ_c = sin⁻¹(0.617) ≈ 38.1°. Since 54° > 38.1°, the angle of incidence exceeds the critical angle. The light does not exit—it undergoes total internal reflection.

Problem 4: An optical fiber has a glass core with n = 1.52 surrounded by cladding with n = 1.41. What is the critical angle at the core-cladding boundary?

Show solution

sin(θ_c) = n_cladding/n_core = 1.41/1.52 = 0.928. θ_c = sin⁻¹(0.928) ≈ 68.1°. Light hitting the boundary at more than 68.1° from the normal is trapped inside the fiber core. Because the indices are close, the critical angle is large, and only nearly grazing rays are totally reflected—this is why fiber optic cables must be kept relatively straight.

8. Mirror Equation and Ray Diagrams

HS-PS4-1 Using Math PS4.A

Mirror equation: 1/f = 1/d_o + 1/d_i Magnification: m = h_i/h_o = −d_i/d_o

Concave Mirror

A concave mirror is converging. A ray parallel to the principal axis reflects through the focal point. A ray through the focal point reflects parallel to the axis. A ray through the center of curvature reflects back on itself.

Convex Mirror

A convex mirror is diverging. Reflected rays spread apart, but their backward extensions meet behind the mirror. Images are virtual, upright, and smaller.

Problem 1: A concave mirror has f = +20 cm. An object is placed 60 cm in front of it. Find d_i and describe the image.

Show solution

1/20 = 1/60 + 1/d_i. 1/d_i = 1/20 − 1/60 = 2/60 = 1/30, so d_i = +30 cm. m = −30/60 = −0.50. The image is real, inverted, and smaller.

Problem 2: A convex mirror has f = −15 cm. An object is 30 cm in front of it. Find d_i and describe the image.

Show solution

1/(−15) = 1/30 + 1/d_i. 1/d_i = −1/15 − 1/30 = −3/30 = −1/10, so d_i = −10 cm. m = −(−10)/30 = +0.33. The image is virtual, upright, and reduced.

9. Thin Lens Equation and Ray Diagrams

HS-PS4-1 Using Math PS4.A

Thin lens equation: 1/f = 1/d_o + 1/d_i Magnification: m = h_i/h_o = −d_i/d_o

Converging Lens

A converging lens is thicker in the middle. A ray parallel to the axis refracts through the far focal point. A ray through the near focal point exits parallel to the axis. A ray through the center travels mostly straight.

Diverging Lens

A diverging lens is thinner in the middle. Refracted rays spread apart. Their backward extensions meet on the object side, forming a virtual, upright, smaller image.

Problem 1: A converging lens has f = +10 cm. An object is placed 30 cm from the lens. Find d_i and magnification.

Show solution

1/10 = 1/30 + 1/d_i. 1/d_i = 1/10 − 1/30 = 2/30 = 1/15, so d_i = +15 cm. m = −15/30 = −0.50. The image is real, inverted, and half the object height.

Problem 2: A diverging lens has f = −20 cm. An object is placed 40 cm from the lens. Find d_i and describe the image.

Show solution

1/(−20) = 1/40 + 1/d_i. 1/d_i = −1/20 − 1/40 = −3/40, so d_i = −13.3 cm. m = −(−13.3)/40 = +0.33. The image is virtual, upright, and reduced.

10. Polarization & Malus’s Law

HS-PS4-3 Using Math PS4.B Cause & Effect

Light is a transverse electromagnetic wave. Unpolarized light has electric field vibrations in many directions perpendicular to travel. Polarized light has vibrations mostly in one direction. A polarizer transmits the component of the electric field aligned with its transmission axis. Polarization is evidence that light behaves as a transverse wave.

Malus’s Law: I = I₀ cos²(θ)

Malus’s Law describes the transmitted intensity of polarized light through an analyzer at angle θ from the light’s polarization direction.

Problem 1: Unpolarized light passes through a single ideal polarizer. What fraction of the original intensity is transmitted?

Show solution

A single ideal polarizer transmits one-half of initially unpolarized light: I = I₀/2.

Problem 2: Polarized light of intensity 80 W/m² passes through a polarizer whose axis is 30° from the light’s polarization direction. What intensity is transmitted?

Show solution

I = 80 cos²(30°) = 80(0.75) = 60 W/m².

Problem 3: What angle reduces polarized light intensity to one-fourth of its original value?

Show solution

I/I₀ = cos²θ = 1/4. Therefore cosθ = 1/2, so θ = 60°.

Problem 4: Unpolarized light with intensity 100 W/m² passes through a polarizer, then through a second polarizer at 45° to the first. What intensity exits?

Show solution

After the first polarizer: I = 50 W/m². Through the second: I = 50 cos²(45°) = 50(0.5) = 25 W/m².

11. Digital Information Transmission

HS-PS4-2 Asking Questions PS4.A PS4.C Stability & Change

Information can be transmitted as either analog or digital signals. Analog signals vary continuously (like a sound wave), while digital signals encode information as discrete values—sequences of ones and zeros. Digital encoding offers major advantages for reliability, storage, and sharing, though it also introduces distinct challenges.

Analog Signals

An analog signal is a continuous wave that mirrors the original information. Vinyl records and AM radio are analog. Noise accumulates with each copy or relay, degrading quality. There is no built-in error correction.

Digital Signals

A digital signal encodes information as binary pulses. Because the receiver only needs to distinguish “on” from “off,” small amounts of noise do not corrupt the message. Digital data can be copied perfectly, compressed, encrypted, and transmitted globally in seconds.

Advantages and Limitations of Digital

Advantages

Signals can be copied without degradation
Error-detection and error-correction codes fix small transmission errors
Data can be compressed for efficient storage
Information can be encrypted for security
Rapid sharing across networks (internet, fiber optics, satellite)

Limitations

Sampling rate and bit depth limit resolution
Requires conversion hardware (analog-to-digital converters)
Data can be accidentally deleted or corrupted en masse
Cybersecurity risks: hacking, data breaches, unauthorized access
Requires power and infrastructure to store and transmit

Discussion: A hospital stores patient records digitally instead of on paper. Evaluate the advantages and disadvantages of this choice. Consider reliability, access, security, and long-term storage.

Show solution

Advantages: Digital records can be backed up in multiple locations (redundancy prevents loss from fire or flood). They can be accessed instantly by authorized staff at any connected facility. Records can be searched, sorted, and cross-referenced far faster than paper. Disadvantages: Digital records are vulnerable to cyberattacks and data breaches—unauthorized access could expose sensitive medical information. A system failure or power outage could temporarily block access. Long-term digital storage requires ongoing maintenance of hardware, software, and file format compatibility. Paper records, while slower to access, do not require electricity and are not vulnerable to hacking.

12. Wave Technology in Everyday Life

HS-PS4-5 Communicating Information PS4.C PS3.D Cause & Effect

Multiple technologies based on wave behavior are part of everyday experience. Each device exploits specific wave properties—reflection, refraction, absorption, emission, interference, or the photoelectric effect—to transmit, capture, or convert energy and information.

Solar Cells

Photovoltaic cells use the photoelectric effect to convert sunlight into electrical energy. Photons with sufficient energy free electrons in semiconductor material, creating a current. Higher-frequency photons carry more energy per photon. Solar cells capture the sun’s energy and produce electricity for homes, vehicles, and satellites.

Wave principle: photoelectric effect, photon energy (E = hf)

Medical Imaging

X-ray imaging uses high-energy EM radiation that passes through soft tissue but is absorbed by dense materials like bone. CT scans combine many X-ray images to create 3D models. MRI uses radio-frequency waves and magnetic fields to image soft tissue without ionizing radiation. Ultrasound uses high-frequency sound waves reflected from tissue boundaries.

Wave principles: absorption, reflection, frequency-dependent penetration

Communications

Cell phones encode voice and data as digital signals carried by radio waves. Wi-Fi uses microwave-frequency radio waves. Fiber optic cables transmit data as pulses of light using total internal reflection. Satellite communications relay microwave signals across continents. Each technology uses wave properties to move information reliably over distance.

Wave principles: EM wave propagation, total internal reflection, digital encoding

Telescopes & Cameras

Optical telescopes use lenses or mirrors to gather and focus light from distant objects, forming magnified images. Digital cameras use photoelectric sensors (CCD or CMOS) to convert focused light into electrical signals, which are stored as digital image files.

Wave principles: refraction, reflection, photoelectric effect, digital storage

Microwave Ovens

Microwave ovens produce EM waves at a frequency (~2.45 GHz) that efficiently transfers energy to water molecules in food. The water molecules absorb the microwave radiation and convert it to thermal energy, heating the food from within.

Wave principle: resonant absorption, EM wave–matter interaction

Communication Task: Choose one technology from this section. In 3–5 sentences, explain to a non-science audience how it uses wave behavior to transmit or capture information or energy. Identify the specific wave property (reflection, refraction, absorption, photoelectric effect, or interference) that makes the technology work.

Example response: Fiber optic internet

Fiber optic cables carry internet data as rapid pulses of laser light through thin glass strands. The glass core has a higher index of refraction than the surrounding cladding, so light hitting the boundary at a steep angle undergoes total internal reflection—it bounces along the fiber without escaping. Because the signal is light rather than electricity, it can travel long distances with very little loss and is immune to electromagnetic interference. The data is encoded digitally: each pulse of light represents a “1” and each gap a “0,” allowing billions of bits per second to flow through a single strand thinner than a human hair.

13. Da Vinci’s Notebook: Waves & Optics Project

HS-PS4-1 HS-PS4-2 HS-PS4-3 HS-PS4-4 HS-PS4-5

Project Goal: Create a scientific notebook in the spirit of Leonardo da Vinci. Your notebook should combine accurate sketches, experimental observations, ray diagrams, calculations, and written explanations of the major ideas in waves and electromagnetic radiation. This project is designed to address all five NGSS HS-PS4 Performance Expectations through hands-on investigation and scientific communication.

Required Project Scope: You will complete 16 total experiments covering wave properties, electromagnetic radiation, and classical optics. At least half of those experiments must prove or explore a mathematical relationship. At least two experiments must involve evaluating a claim or comparing models (wave vs. particle). They should include use of the wave equation (v = fλ), Snell’s Law, the thin lens or mirror equation, magnification, Malus’s Law, and photon energy (E = hf).

Required Notebook Structure

Each experiment gets its own notebook entry. The goal is not to copy a lab sheet. The goal is to show that you can observe a wave or optical phenomenon, draw it clearly, explain what happened, and connect the observation to the physics.

Apparatus Sketch

Draw the actual setup: light source, lens or mirror, screen, ray box, ruler, polarizer, protractor, optical bench, slit, or diffraction grating. Label distances, angles, and important parts.

Phenomenon Sketch

Draw what the wave or light does. Include normal lines, principal axes, focal points, centers of curvature, image locations, ray directions, or wave patterns where appropriate.

Written Method

Explain how the experiment was performed clearly enough that another student could repeat it without guessing.

Results and Claim

State what you observed or measured. Then make a physics claim explaining what law, equation, or pattern your experiment supports. For claim-evaluation experiments, state the claim, the evidence, and your reasoning.

Suggested Set of 16 Experiments

Use classroom wave and optics materials to complete these investigations. Your teacher may adjust the exact list based on available equipment, but your final notebook should include 16 completed entries.

#	Experiment	NGSS Focus	Mathematical / Diagram Focus
1	Wave speed on a spring or string	HS-PS4-1	v = fλ; measure frequency and wavelength, calculate speed
2	Frequency–wavelength relationship for sound	HS-PS4-1	v = fλ; use tuning forks of known frequency to find λ
3	Law of reflection with a plane mirror	HS-PS4-1	θ_i = θ_r; normal line and measured angles
4	Refraction from air into water or acrylic	HS-PS4-1	Ray bends toward/away from normal; qualitative ray diagram
5	Snell’s Law investigation	HS-PS4-1	n₁sinθ₁ = n₂sinθ₂
6	Total internal reflection and critical angle	HS-PS4-1 HS-PS4-5	Critical angle calculation; fiber optics connection
7	Thin lens equation on the optical bench	HS-PS4-1	1/f = 1/d_o + 1/d_i; solve for focal length
8	Magnification with a converging lens	HS-PS4-1	m = h_i/h_o = −d_i/d_o
9	Concave mirror image formation	HS-PS4-1	Mirror equation and ray diagram for a real image
10	Diffraction through a single slit	HS-PS4-3	Wave model evidence: light spreading beyond slit width
11	Double-slit interference pattern	HS-PS4-3	Constructive/destructive interference; wave model evidence
12	Polarization through one and two filters	HS-PS4-3	Malus’s Law: I = I₀cos²θ; transverse wave evidence
13	Photoelectric effect simulation	HS-PS4-3	Particle model evidence: threshold frequency, E = hf
14	EM spectrum and photon energy investigation	HS-PS4-4	Calculate E = hf for different EM regions; evaluate a radiation claim
15	Digital vs. analog signal comparison	HS-PS4-2	Signal degradation with noise; advantages of digital encoding
16	Technology research: how a device uses waves	HS-PS4-5	Technical communication: solar cell, MRI, fiber optics, or similar

Mathematical Experiment Requirement

At least 8 of the 16 experiments must do more than describe what happened. They must use a measured value, calculated value, graph, or equation-based comparison. Strong choices include v = fλ, Snell’s Law, critical angle, thin lens equation, magnification, mirror equation, Malus’s Law, and E = hf.

Claim and Model Evaluation Requirement

At least 2 of the 16 experiments must involve evaluating a claim or comparing models. For example: use diffraction and interference results to argue that the wave model explains what you observe, then use photoelectric effect results to argue for the particle model. For the EM spectrum experiment, find a published claim about radiation and evaluate it using E = hf and the concept of ionization.

Optical Bench Investigation

Use the optical bench to test the thin lens equation. Mount a light source, a lens, and a screen. Adjust the screen until a clear image appears. Record object distance, image distance, and image orientation. Repeat for several object distances and compare your measured focal length to the lens label. For the notebook, include a careful sketch of the physical apparatus and a separate ray diagram showing why the image forms where it does.

Grading Rubric

Category	Excellent Evidence	Points
Sketches and Diagrams	Each of the 16 experiments includes an apparatus sketch and a phenomenon/ray/wave diagram where appropriate. Diagrams are accurate, labeled, organized, and use color or line style to distinguish rays, normals, axes, focal points, wavefronts, and images.	25
Methods	Notebook explains how each setup was built and how measurements were taken. The explanation is specific enough that another group could repeat the procedure.	15
Results and Calculations	All 16 experiments include observations and claims. At least 8 experiments include meaningful mathematical work using measured values, calculated values, graphs, or equation-based comparisons.	25
Claims and Arguments	At least 2 experiments include a structured claim–evidence–reasoning argument evaluating a scientific claim or comparing wave vs. particle models. Reasoning connects evidence to the appropriate model or equation.	15
Organization and Craft	Notebook has a consistent visual style, clear headings, revised work, and a finished Da Vinci-inspired scientific journal appearance.	20

NGSS Alignment Summary

Performance Expectation	Addressed By Experiments
HS-PS4-1 Mathematical wave relationships	1, 2, 3, 4, 5, 6, 7, 8, 9
HS-PS4-2 Digital information	15
HS-PS4-3 Wave and particle models	10, 11, 12, 13
HS-PS4-4 Radiation effects on matter	14
HS-PS4-5 Wave technology	6, 16

Final Reflection Questions

Which wave or optical phenomenon was easiest to represent with a diagram? Which was hardest?
Where did your physical observations agree with the equations? Where did experimental uncertainty appear?
For the diffraction and photoelectric experiments, which model (wave or particle) did each support? Why can’t a single model explain both?
What are two advantages and two limitations of digital information storage compared to analog?
Choose one wave-based technology. How would our daily life change if that technology did not exist?
What would you improve if you could redesign one experiment?

Note: Solutions are hidden in expandable sections so students can check their work after attempting each problem. This unit addresses NGSS HS-PS4: Waves and Electromagnetic Radiation. Standards information from nextgenscience.org.