IB Physics SL C.3 Wave phenomena Questions

SLSL HLHL

Use wavefront and ray diagrams to trace boundary behaviour, combine coherent waves, and calculate fringe positions in Young double-slit setups.

152 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Relate a ray to energy propagation and a wavefront to equal-phase points; rays are perpendicular to wavefronts for transverse and longitudinal waves.
Continue transmitted wavefronts with correct orientation, curvature, continuity at the boundary and wavelength spacing consistent with changed speed.
Construct reflected rays using the local normal and equal angles, checking that the actual reflected path reaches the observer or receiver.
Explain undeflected entry along a radius of a semicircular block; for a supplied thin central-ray approximation, compare the two nearly parallel surfaces.
Apply Snell’s law using ray angles measured from the normal; convert a wavefront-to-normal angle to its complement before substitution.
Use refractive index or speed to predict bending and check wavefront spacing: slowing bends towards the normal and shortens wavelength at fixed frequency.
Combine n=c/v with refraction data or travel time to determine medium speed and refractive index, converting cable length and delay units.
At a stationary interface keep frequency fixed and use n1λ1=n2λ2; a higher index gives lower speed and shorter wavelength.
Multiply successive relative indices by cancelling the intermediate speed; compare inverse index ratios and retain precision for close-index subtraction.
When wavelength-dependent indices are supplied, use them to compare ray speed, travel time or refraction without assuming an unprovided dispersion profile.
For a Snell-law graph, identify which sine is vertical before reading index from slope; use limiting slopes for its absolute uncertainty.
State both total-reflection conditions and distinguish the critical grazing case: incident medium has higher index, and incidence must exceed critical.
Use sinθc=n2/n1 with the actual receiving medium, rearranging for angle or unknown index; only substitute 1 when that medium is air.
Justify non-emergence by comparing actual internal incidence with critical, or by showing that a refracted-angle sine would exceed one.
For a limiting fibre entrance angle, take the complement of wall critical incidence, then apply Snell’s law at the entrance surface.
Trace confined light with sensible entry refraction and equal reflection angles; rays entering above the acceptance limit can pass into the cladding.
Explain why close core and cladding indices give a critical angle near 90° and confine only nearly axial rays.
Connect critical angle to a medium-to-air speed or an air-to-glass sine-graph slope: v=c sinθc and sinθc=1/n.
Apply a transmission cutoff to sound using the given speed ratio, obtaining incidence from the actual ray geometry or equivalent wavefront angle.
Define superposition by adding signed displacements at the same point and time; amplitude or crests-and-troughs wording alone is insufficient.
Add pulse shapes point by point in the overlap region and preserve each pulse after passage; zero resultant does not destroy the original pulses.
Build a resultant graph from simultaneous signed values, checking zeros, endpoints and extrema; read its amplitude rather than adding separated peaks.
Translate travelling profiles by speed × elapsed time before locating the largest sum; use relative time offsets on paired graphs independently of signs.
Define coherence through phase difference constant over time, explain a stable pattern and identify how a common source or split wavefront supplies it.
For initially in-phase sources, relate integer and half-odd wavelength path differences to reinforcement and cancellation, specifying arrival phase clearly.
Calculate each propagation path before subtraction, using geometry or both reflection legs; compare the difference with the wavelength.
Include initial source phase as well as propagation phase: equal paths can stay dark for antiphase sources, while a half-odd path can then reinforce.
Distinguish minimum from zero: at antiphase subtract arriving amplitudes, and consider extra reflected waves before claiming complete cancellation.
Explain why double slits produce a fringe pattern and how a supplied light-sensor response maps intensity maxima into measured voltage peaks.
Read spatial graphs with the correct meaning: source-motion peak spacing can equal wavelength, while ripple-pattern fringe width runs across equivalent bands.
Predict wavelength-dependent pattern changes and count maxima by path order; treat two colours as separate patterns and check their possible coincidences.
Sketch an ideal narrow double-slit intensity pattern with equal-height repeated maxima and zero minima over the stated scale; explain energy redistribution.
Apply s=λD/d to adjacent equivalent fringes, using compatible units and rearranging for the unknown distance, geometry ratio or wavelength.
Recognise half-fringe and multiple-gap measurements before substitution: double central-bright to first-dark distance and count gaps between fringe centres.
Identify whether an angular request is one-sided, a total span or a change; compare the same fringe type and order when scaling with wavelength.
Use proportional changes or straight-line plots to interpret Young’s equation; for fringe encounter rate divide observer speed by spatial spacing.
Relate diffraction spreading qualitatively to wavelength and aperture: shorter wavelengths spread less, while longer radio waves require larger apertures.

Covered syllabus points

C.3.1—Wavefronts and rays C.3.2—Snell’s law C.3.3—Refractive index C.3.4—Total internal reflection C.3.5—Superposition C.3.6—Coherence C.3.7—Path difference C.3.8—Two-source interference C.3.9—Young double-slit equation C.3.10—Reflection, refraction and transmission at boundaries C.3.11—Diffraction around bodies and through apertures

[Maximum number: 1]

A group of students is investigating refraction in a semi-circular glass block.

Light from a ray box enters the curved side of the block. The light passes through the block and leaves, refracted, at P .

Outline how the students can ensure that the light is not deflected at the curved surface.

measure P to be at the centre of the flat edge/side so that incident rays are aimed at P /go through radial lines

OR

check that the incident angle is $0^{\circ}$ at every point of incidence

[1]

[Maximum number: 6]

Monochromatic light enters the base of a plastic beaker that contains water with an oil layer floating on it. A student draws a diagram to show the directions the light takes as it passes through the layers. The student's diagram has one error at position A and one error at position B. The refractive indices of the materials are shown on the diagram.

The light is refracted at an angle of $32^{\circ}$ when it enters the plastic layer as shown.

(a)

Identify, with a reason, the error in the student's diagram for

[ 4 ]

(i)

light crossing the plastic-water interface (position A).

[ 2 ]

the angle of refraction ought to be greater than the angle of incidence OR the ray should refract away from the normal
because ray goes from high refractive index/<<optically>> more dense/slower medium to
low refractive index/optically less dense/faster medium

Marking guidance:

Do not allow use of e.g $n_{1}$
unless medium one is
described e.g. $n_{\text {air }}$

(ii)

light at the water-oil interface (position B).

[ 2 ]

(b)

Calculate the angle of incidence at the air-plastic interface.

[ 2 ]

$\begin{aligned} \text { Use of Snell's Law }<\frac{\sin i}{\sin r}=\frac{1.60}{1} \gg i=\sin ^{-1}<1.60 \times \sin 32^{\circ}>=58<^{\circ} \gg \end{aligned}$

'Use of' requires a substitution NOT just a statement of a formula

Accept 1.0 rad (unit must be included to show a deliberate attempt to use rad rather than a calculator mistake)

[Maximum number: 2]

They plot a graph of the variation with the sine of $\theta_{i}$ of the sine of $\theta_{r}$ .
They add uncertainty bars for $\sin \theta_{r}$ for the first and last data point and draw the best-fit line.

Determine the value of the refractive index of the glass with its absolute uncertainty.

States gradient gives the value of the refractive index

OR

n=1.5 $n=1.5 \pm 0.2$

MP1 can be shown as an equation.

Candidates may calculate the uncertainty by using the gradient of the line found in cii) or finding the average of the max and min lines of best fit.

Look for working leading to $0.1 \leq \Delta n \leq 0.2$ .

[Maximum number: 2]

The light is refracted at an angle of $32^{\circ}$ when it enters the plastic layer as shown.

Calculate the critical angle for the plastic-water interface.

$\begin{aligned} \frac{\sin i}{\sin r}=\frac{1.33}{1.60} \text { and } \sin r=1 i=\lessdot \sin ^{-1} 0.831 »=56<^{\circ} \gg \end{aligned}$

Accept 0.98 rad (unit required)

[Maximum number: 3]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

A second loudspeaker S emits the same frequency as L but vibrates out of phase with L . The graph below shows the variation with time t of the displacement x of the waves emitted by S and L .

On the graph, sketch the variation with t of x for the wave formed by the superposition of the two waves. be marked.

Agreement at all zero displacements.
Maxima and minimum at correct times.
Constant amplitude of $1.60\ \text{mm}$ .

Figure for Answer to Question 1 — IB Physics SL

[Maximum number: 1]

This question is about interference.

Light from a laser is incident on two identical parallel slits. The light from the two slits produces a fringe pattern on a screen.

A central bright fringe is produced at C . The next bright fringe is produced at A . There is a dark fringe at B .

The light from the laser is coherent and monochromatic. Outline what is meant by the term

coherent.

[Maximum number: 1]

This question is about interference.

Light from a laser is incident on two identical parallel slits. The light from the two slits produces a fringe pattern on a screen.

A central bright fringe is produced at C . The next bright fringe is produced at A . There is a dark fringe at B .

The distance from the two slits to the screen is 1.5 m . The distance BC is 1.8 mm and the distance between the slits is 0.30 mm .

State the path difference, in metres, between the waves that meet at B .

Exam points

Explain two-source maxima and minima by overlapping waves and their arrival phase; for in-phase sources link these to integer and half-odd path differences.
Explain why two narrow slits form many fringes: diffraction lets their waves overlap, then interference creates bright and dark positions.
Use a supplied detector model to interpret a measured signal: where sensor voltage is proportional to light intensity, voltage peaks mark interference maxima.
Calculate arriving amplitude from path difference and the individual amplitudes; at antiphase subtract amplitudes, so unequal waves need not cancel completely.
Choose a possible wavelength by expressing a destructive path difference as a half-odd number of wavelengths, with consistent distance units.
Give arrival phase in degrees or radians, not wavelengths: a dark fringe can correspond to π rad while its path difference is λ/2.
When one source moves directly away from a detector, read wavelength from successive intensity maxima because only that source’s path changes.
Identify fringe width across adjacent equivalent interference bands, rather than confusing it with wavelength measured along propagation.
Sketch the ideal narrow-slit two-source pattern with repeated equal-height, equally spaced maxima and zero minima over the stated graph scale.
At fixed geometry, shorter wavelength narrows fringe spacing and doubling wavelength doubles it; compare the same fringe order when making this change.
For two incident colours, retain each pattern separately: the longer wavelength has wider spacing, and some bright positions can coincide.
Count maxima using path-difference orders as a microphone moves toward an equal-path line; include the maximum at the endpoint when asked.
Along an equal-path line, preserve the initial source phase: sources already in antiphase can remain at a minimum throughout.
Distinguish a faint destructive minimum from complete cancellation; unequal arriving amplitudes or extra wall-reflected waves can leave a signal.
Explain dark fringes through energy redistribution toward bright maxima; destructive interference does not remove the total wave energy.
For the first dark double-slit fringe, use half the bright-fringe spacing when applying s=λD/d to obtain its distance from the centre.
Compare each detector’s two paths with the wavelength independently before labelling its signal a maximum or minimum.

[Maximum number: 1]

This question is about interference.

Light from a laser is incident on two identical parallel slits. The light from the two slits produces a fringe pattern on a screen.

A central bright fringe is produced at C . The next bright fringe is produced at A . There is a dark fringe at B .

State the phase difference between the light waves from the two slits that meet at B .

$180^{\circ} / \pi \mathrm{rad}$ ;

Marking guidance:

Do not accept $\frac{\lambda}{2}$ .

[Maximum number: 3]

This question is about interference.

Light from a laser is incident on two identical parallel slits. The light from the two slits produces a fringe pattern on a screen.

A central bright fringe is produced at C . The next bright fringe is produced at A . There is a dark fringe at B .

The distance from the two slits to the screen is 1.5 m . The distance BC is 1.8 mm and the distance between the slits is 0.30 mm .

Show that the laser produces light of wavelength equal to 720 nm .

use of $\lambda=\frac{s d}{D}$ ;
$s=\underline{2} \times 1.8(\mathrm{~mm})$ ;
(award this mark for any evidence for the factor of 2 )
$\lambda=\frac{2 \times 1.8 \times 10^{-3} \times 0.30 \times 10^{-3}}{1.5} /$ OWTTE;
( $=7.2 \times 10^{-7} \mathrm{~m}$ )

Exact answer is given, award marks for correct working.

[Maximum number: 2]

This question is about diffraction and resolution.

Monochromatic light is incident normally on a single narrow slit and gives rise to a diffraction pattern on a screen.

Two lamps emit light of wavelength 620 nm . The lights are observed through a circular aperture of diameter 1.5 mm from a distance of 850 m . Calculate the minimum distance between the lamps so that they are resolved.

equating $1.22 \frac{\lambda}{b}$ to $\frac{x}{D}$ ;
0.43 (m);

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