05.10 Waves and Optics Exam Review

Module 05: Waves and Optics · quiz worth 80 pts

The big idea The exam asks you to connect wave models, diagrams, equations, and technologies: identify the physical situation first, then choose the matching representation and check the result.

Identify the situation before the formula

The exam mixes several equations with similar symbols.

Not sure about the basics underneath this lesson?

Formula map

Period and frequency
f=1Tf=\frac{1}{T}

T in seconds; f in hertz.

Wave speed
v=fλv=f\lambda

v in m/s, f in Hz, λ in m.

Pendulum period, small angle
T=2πLgT=2\pi\sqrt{\frac{L}{g}}

L is pivot to bob center; mass does not appear.

Lens or mirror equation
1f=1do+1di\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}

Positive dᵢ is real; negative dᵢ is virtual under this module's convention.

Magnification
m=−didom=-\frac{d_i}{d_o}

Sign gives orientation; |m| gives size ratio.

Refractive index
n=cvn=\frac{c}{v}

n has no unit.

Snell's law
n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1=n_2\sin\theta_2

Angles are measured from the normal.

Double-slit bright fringe
xm=mλLdx_m=\frac{m\lambda L}{d}

Small-angle model; m = 1 for the first bright fringe.

Critical angle
sin⁡θc=n2n1\sin\theta_c=\frac{n_2}{n_1}

Only for light traveling from n₁ > n₂.

Wave model and behavior

Mechanical waves require a medium; electromagnetic waves do not. Transverse disturbance is perpendicular to travel; longitudinal disturbance is parallel. Amplitude tracks maximum displacement and often energy or intensity, while frequency is cycles per second and period is seconds per cycle. At a boundary, frequency stays fixed while speed and wavelength may change. Reflection returns a wave, refraction changes direction with speed, diffraction spreads a wave around edges, and interference follows superposition. Beats are time-varying loudness from nearby frequencies; Doppler shift is a detected frequency change from relative motion.

Optics decision tree

Ray diagram

Mark the axis, device, F, 2F, and object. Draw two named principal rays from the object tip. Use dashed lines only for backward extensions.

Image equation

Predict the image region, list signed distances in one unit, solve the reciprocal equation, then interpret dᵢ and m.

Refraction

Draw the normal, label incident side 1 and transmitted side 2, predict toward or away, then use Snell's law in degree mode.

Critical angle

First confirm the ray starts in the higher-index medium. Then set the refracted angle to 90° or use sin θc = n₂/n₁.

Interference

Identify fringe order and what x measures. Convert every length to compatible units before using xₘ = mλL/d.

Not sure about this bit?

Technology connections

Optical fibers use total internal reflection. Polarizers select transverse vibration directions. Prisms disperse white light because index varies with wavelength. Wireless systems encode information on electromagnetic carriers and manage spectrum to limit interference. Digital symbols can be regenerated and checked for errors, but still face noise and bandwidth limits. Radio telescopes focus radio waves onto receivers. Photovoltaic cells turn absorbed photon energy into mobile charge and electrical output.

Mixed worked examples

Wave from frequency and wavelength

  • Frequency. f=4.0 Hzf=4.0\,\text{Hz}
  • Wavelength. λ=1.5 m\lambda=1.5\,\text{m}

Find wave speed.

  1. Multiply frequency by wavelength.
    v=fλ=(4.0)(1.5)=6.0 m/sv=f\lambda=(4.0)(1.5)=6.0\,\text{m/s}

v = 6.0 m/s.

Concave-mirror image

  • Focal length. f=12 cmf=12\,\text{cm}
  • Object distance. do=36 cmd_o=36\,\text{cm}

Find dᵢ and describe the image.

  1. Subtract reciprocals.
    1di=112−136=118\frac{1}{d_i}=\frac{1}{12}-\frac{1}{36}=\frac{1}{18}
  2. Take the reciprocal and find m.
    di=18 cm,m=−1836=−0.50d_i=18\,\text{cm},\qquad m=-\frac{18}{36}=-0.50

The image is real, inverted, and half-size between f and 2f.

Refraction check

  • Air. n1=1.00n_1=1.00
  • Water. n2=1.33n_2=1.33
  • Incident angle. θ1=30.0∘\theta_1=30.0^\circ

Find θ₂.

  1. Apply Snell's law.
    θ2=sin⁡−1 ⁣(1.00sin⁡30.0∘1.33)=22.1∘\theta_2=\sin^{-1}\!\left(\frac{1.00\sin30.0^\circ}{1.33}\right)=22.1^\circ

The smaller angle matches bending toward the normal.

Exam traps

Wrong angle reference

Measure refraction and reflection angles from the normal, not the surface.

Wrong reciprocal result

After finding 1/dᵢ, take the reciprocal to find dᵢ.

Doppler versus loudness

Motion changes detected frequency through wavefront spacing. Distance mainly changes intensity.

Beats versus standing waves

Beats are amplitude variation from nearby frequencies. Standing waves require fixed nodes and antinodes.

Digital versus carrier

Digital describes discrete representation, not a unique kind of wave or channel.

Unit drift

Convert nm, cm, and cycle timing before substituting; attach the requested unit to the answer.

Exam-day workflow

Before opening the exam

Put your notebook in order. Have the calculator, ruler, and protractor named by the source ready.

For a concept item

Name the mechanism and state a cause-and-effect chain. Eliminate choices that change the wrong quantity.

For a diagram

Add the axis or normal first, label reference points, and draw carefully with the ruler and protractor.

For a calculation

Write the unknown, list values with units, choose one equation, rearrange, substitute, and check direction and size.

Before submitting

Revisit marked questions, check signs and units, and make sure every item has a response.

Mixed exam practice

Work on paper before opening each explanation. These are study checks, not copied exam questions.

Final checklist

Tick these off as you go. Saved in this browser.