Atlas MCAT Course

Equations & How to Use Them → Equations: Waves, Optics & Modern Physics

Equations: Waves, Optics & Modern Physics

Waves, lenses, photons, decay, and absorbance.

01The idea

When energy propagates through space or media — or when matter interacts at small scales.

THREAD · Structure → function

02Build the model

AWave speed

v = fλ

Use when: any wave is described (sound, light, water); frequency or wavelength changes.

BDoppler effect (conceptual)

Use when: the source or observer is moving; a pitch or frequency shift is described.

CSound intensity level

β = 10 log(I / I₀)

Use when: decibels are mentioned; loudness comparisons are made.

DThin lens equation and magnification

1/f = 1/dₒ + 1/dᵢ

m = −dᵢ / dₒ

Use when: lenses or mirrors are involved; images are formed (eye, microscope); image size or orientation matters.

ESnell’s law

n₁ sin θ₁ = n₂ sin θ₂

Use when: light crosses boundaries; refraction or bending is discussed.

FPhoton energy and the photoelectric effect

E = hf = hc / λ

Use when: light interacts with electrons; frequency matters more than intensity; light ejects electrons; threshold frequency is mentioned.

GRadioactive decay and half-life

N = N₀e^(−λt)

N = N₀(½)^n

Use when: decay over time; continuous decay is implied; half-lives are counted (stepwise decay questions).

HBeer–Lambert law: absorbance, concentration, path length

A = εlc

Use when: UV/Vis, absorbance, concentration determination.

03See the connections

The lesson names these links itself. Read the map left to right.

Waves

v = fλ
Doppler
Decibels

Optics

Thin lens, magnification
Snell’s law

Small scales

E = hf
Decay, half-life
Beer–Lambert

Next: data and statistics.

04Reason with it

Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.

Think first.

A sample has 1/8 of its original radioactive nuclei left. How many half-lives have passed?

Think first.

Dim UV light ejects electrons from a metal, but bright red light doesn’t. Why?

Think first.

A solution’s concentration doubles in the same cuvette. What happens to absorbance?

Think first.

A lens gives a negative magnification. What does that tell you?

05MCAT lens

MCAT shortcuts

Faster wave → longer wavelength if frequency fixed

Moving closer → higher frequency

+10 dB = 10× intensity

Higher index → bends toward normal

Frequency sets photon energy

Decay is exponential; absorbance ∝ concentration

06Common traps

Trap 1: Brighter light means more energetic photons

Misconception

Brightness is photon number.

Correct model

Frequency sets photon energy.

Trap 2: Radioactive decay is linear

Misconception

It is exponential.

Correct model

Each half-life halves what remains.

Trap 3: Decibels add linearly

Misconception

They are logarithmic.

Correct model

+10 dB = 10× intensity.

07Dependency check

Can you reconstruct this concept without looking at the page? You should now be able to reason through:

How wave speed, frequency, and wavelength relate

Check against 02 · A.

How lenses form images

Check against 02 · D.

What sets photon energy

Check against 02 · F.

How decay and absorbance scale

Check against 02 · G and H.

If something feels unclear, the missing idea is usually thisFrequency is set by the source; the medium sets speed and wavelength; frequency sets photon energy.

08Remember

REMEMBER · if you keep only a few things

v = fλ.
β = 10 log(I/I₀): +10 dB = 10×.
1/f = 1/dₒ + 1/dᵢ; m < 0 inverted.
n₁ sin θ₁ = n₂ sin θ₂.
E = hf; no threshold, no electrons.
N = N₀(½)^n; A = εlc.

09Forward hook

The last equation block isn’t about physics at all: it’s about reading data.

How is data summarized, compared, and interpreted?

That leads to statistics and experimental design.

Next lesson
Equations: Data & Statistics→