IB Physics HL C 3 Wave Phenomena Questions

Use ray and wavefront diagrams to trace boundary changes, calculate interference fringes, and explain how aperture width shapes a diffraction pattern.

Exam points

Apply n₁sinθ₁ = n₂sinθ₂ and n = c/v to calculate refraction angles, wave speed or wavelength.
Use sinθc = n₂/n₁ to decide whether a ray undergoes total internal reflection at a boundary.
Read wavefront and ray diagrams to predict reflection, refraction or transmission at an interface.
Apply superposition to add overlapping displacements and compare resultant amplitudes or intensities.
Use coherence and path difference to identify constructive or destructive interference at a point.
Apply s = λD/d to calculate Young double-slit fringe spacing or infer wavelength and slit separation.
Predict how wavelength and aperture width change diffraction spreading and a single-slit central maximum.
Interpret double-slit intensity patterns shaped by a single-slit envelope, including missing maxima.
Apply nλ = d sinθ to determine diffraction-grating orders and compare spectral-line angles.

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 C.3.12 (HL)—Single-slit diffraction C.3.13 (HL)—Diffraction envelope C.3.14 (HL)—Diffraction gratings

[Maximum number: 2]

A converging lens is placed between an object and a screen. An image of the object is formed on the screen.

(a)

Draw a ray to locate the focal point of the lens. Label this point with the letter F .

[ 1 ]

(b)

The lens suffers from spherical aberration.

[ 1 ]

(i)

Draw lines to complete the rays in the diagram.

[ 1 ]

[Maximum number: 12]

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 ]

Use of Snell's Law « $\frac{\sin i}{\sin r}=\frac{1.60}{1}$ »
$i=\sin ^{-1} \ll 1.60 \times \sin 32^{\circ}>=58<^{\circ} \gg$

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

Marking guidance:

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

(c)

Calculate the critical angle for the plastic-water interface.

[ 2 ]

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

Accept 0.98 rad (unit required)

(d)

Monochromatic light of wavelength $6.3 \times 10^{-7} \mathrm{~m}$ in air is incident from above at a normal to the oil layer. Rays on the diagram are shown at near-normal incidence for clarity. Three positions X, Y and Z are shown on the diagram.

[ 4 ]

(i)

Identify, with a reason, a position at which there is a phase change of $180^{\circ}$ .

[ 1 ]

(ii)

Determine the minimum thickness of the oil layer for which light is not reflected. State your answer to an appropriate number of significant figures.

[ 3 ]

Use of $2 d \mathrm{n}=m \lambda$ $2.1 \times 10^{-7}$ «m»

any answer to 2 s.f.

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

[Maximum number: 12]

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

(a)

The beam is incident normally on a double slit. The distance between the slits is 0.300 mm . A screen is at a distance D from the slits. The diffraction angle $\theta$ is labelled.

[ 6 ]

(i)

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

[ 3 ]

superposition of light from each slit / interference of light from both slits with path/phase difference of any half-odd multiple of wavelength/any odd multiple of $\pi$ (in words or symbols), producing destructive interference

(ii)

Outline why the beam has to be coherent in order for the fringes to be visible.

[ 1 ]

(iii)

The wavelength of the beam as observed on Earth is 633.0 nm . The separation between a dark and a bright fringe on the screen is 4.50 mm . Calculate D.

[ 2 ]

evidence of solving for D: $D=\frac{s d}{\lambda}$ $D=\frac{4.50\times10^{-3}\times0.300\times10^{-3}}{633.0\times10^{-9}}\times2=4.27\ \mathrm m$

(b)

The graph of variation of intensity with diffraction angle for this experiment is shown.

[ 3 ]

(i)

Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.

[ 3 ]

$\begin{aligned} \sin\theta=\frac{4\times633.0\times10^{-9}}{0.300\times10^{-3}} \\ \theta=0.00844 \end{aligned}$

(c)

The air between the slits and the screen is replaced with water. The refractive index of water is 1.33 .

[ 3 ]

(i)

Calculate the wavelength of the light in water.

[ 1 ]

$\frac{633.0}{1.33}=476\ \mathrm{nm}$

(ii)

State two ways in which the intensity pattern on the screen changes.

[ 2 ]

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Covered syllabus points

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