C.3 Wave phenomena: IB Physics HL exam-style questions

Monochromatic light passes through a single slit and forms a diffraction pattern on a distant screen. The slit width is doubled and the wavelength is halved.

What happens to the width of the central maximum?

Monochromatic light passes through two slits and forms an interference pattern on a distant screen. The pattern of bright fringes is modulated by the single-slit diffraction pattern of each slit.

The width of each slit is now reduced while the separation of the centres of the slits is kept the same. Which row describes the change in the separation of adjacent bright fringes and in the number of bright fringes within the central maximum of the diffraction envelope?

Monochromatic light is incident normally on a diffraction grating. The second-order maximum is observed at an angle of 30.0° to the straight-through direction.

What is the angle of the first-order maximum?

A ray of light passes from medium X into medium Y. The diagram, drawn on a square grid, shows the incident ray, the refracted ray and the normal at the point of incidence.

What is the ratio (wavelength of the light in Y)/(wavelength of the light in X)?

An equilateral glass prism PQR is completely immersed in water of refractive index 1.33. A ray of light enters face PQ along the normal and then strikes face PR, as shown.

What is the least refractive index of the glass for which the ray is totally internally reflected at PR?

Two loudspeakers S₁ and S₂, 3.0 m apart, emit sound of wavelength 1.0 m in phase. A microphone is placed 4.0 m from S₁ along a line perpendicular to S₁S₂.

What is detected at the microphone?

Two coherent sources each produce waves of intensity I₀ at a point P. The waves arrive at P in phase. The intensity of a wave is proportional to the square of its amplitude.

What is the intensity at P?

In a double-slit experiment the slits are 0.50 mm apart and the screen is 2.0 m from the slits. The diagram shows the bright fringes seen on the screen and the distance between the centres of the two outermost bright fringes.

What is the wavelength of the light?

The diagram shows wavefronts of a wave passing from medium 1 into medium 2. The wavefront spacing is 1.5 cm in medium 1 and 1.0 cm in medium 2.

What is the ratio n₂/n₁ of the refractive index of medium 2 to that of medium 1?

Two loudspeakers are connected to the same signal generator, but the leads to one of them are reversed, so that the speakers emit sound of wavelength λ in antiphase.

At which of the following path differences from the two speakers is the sound a minimum?

Light of wavelength 500 nm passes through a single slit and forms a diffraction pattern on a screen 2.00 m from the slit. The graph shows how the intensity on the screen varies with the distance y from the centre of the pattern.

What is the width of the slit?

Straight water waves of wavelength 2.0 cm approach a gap of width 10 cm in a barrier, as shown. The gap is then narrowed to 2.0 cm while the frequency of the waves is kept constant.

Which row describes the waves beyond the narrower gap, compared with those beyond the 10 cm gap?

A layer of cooking oil of refractive index 1.47 floats on water of refractive index 1.33 in a glass dish. The oil and water surfaces are horizontal. A ray of light in air strikes the oil surface at an angle of incidence of 50°.

What is the angle between the ray in the water and the normal?

Monochromatic light is incident normally on two narrow slits a distance d apart, and the pattern is observed on a distant screen. The two slits are then replaced by a diffraction grating with many slits, also a distance d apart, illuminated by the same light.

Which statements about the principal maxima of the grating pattern, compared with the maxima of the two-slit pattern, are correct?

I. They are at the same angles.

II. They are narrower.

III. They are further apart.

Two pulses travel towards each other along a stretched rope, each at a speed of 20 cm s⁻¹. The diagram shows the rope at time t = 0.

What is the displacement of point P at t = 2.0 s?

The two headlamps of a parked car illuminate the same white wall, but no interference fringes can be seen where the two beams overlap.

Which statement explains this?

Two loudspeakers connected to the same signal generator emit sound of frequency 680 Hz in phase. The speed of sound is 340 m s⁻¹. A student walks along a line parallel to the line joining the speakers, starting at the central loud point, and passes through three quiet points.

What is the path difference from the two speakers at the third quiet point?

Sound travels at 340 m s⁻¹ in air and at 1500 m s⁻¹ in water. Total internal reflection of sound can occur at a flat air–water surface.

Which row gives the critical angle, and the medium in which the sound must be travelling towards the surface?

A discharge lamp emits two monochromatic lines of wavelength 440 nm and 660 nm. The light is incident normally on a diffraction grating with 250 lines per mm.

What is the smallest non-zero angle at which a maximum of one wavelength coincides with a maximum of the other?

An upward pulse travels along each of two long horizontal ropes towards the right-hand end of the rope. Rope 1 is tied to a rigid wall. Rope 2 is tied to a light ring that can slide without friction on a smooth vertical pole, so that this end is free to move.

Which row describes the reflected pulse on each rope?

In a double-slit experiment with monochromatic light the fringe spacing on the screen is s. The whole apparatus, including the slits and the screen, is then immersed in water of refractive index 1.33. The light source, the slit separation and the slit-to-screen distance are unchanged.

What is the new fringe spacing?

White light containing all wavelengths from 400 nm to 700 nm is incident normally on a diffraction grating with 300 lines per mm. Complete spectra are formed on both sides of the central maximum.

Which statements are correct?

I. The first-order spectrum and the second-order spectrum overlap.

II. The second-order spectrum and the third-order spectrum overlap.

III. In each spectrum, violet light is diffracted through a smaller angle than red light.

Two coherent sources S₁ and S₂ emit waves of wavelength λ in phase. At point P the path difference from the two sources is 1.5λ. At P, the wave from S₁ alone would have amplitude 2A and the wave from S₂ alone would have amplitude A. The intensity at P due to S₁ alone is I₁. The intensity of a wave is proportional to the square of its amplitude.

What is the intensity at P when both sources emit?

A straight optical fibre has a core of refractive index 1.50 and a cladding of refractive index 1.40. A ray of light in air strikes the flat end face of the core at an angle θ to the axis of the fibre, as shown, and refracts into the core.

What is the largest value of θ for which the ray is totally internally reflected at the core–cladding boundary?

Straight water waves of wavelength λ travel across a lake and pass a small rocky island whose width is similar to λ.

Which statements about the waves beyond the island are correct?

I. The waves spread into the region directly behind the island.

II. The wavelength of the waves directly behind the island is less than λ.

III. If the island were the same size but λ were larger, the waves would spread further into the region behind it.

Straight water waves travel from shallow water into deep water, where they travel faster. The boundary between the two regions is straight.

Which diagram shows the wavefronts and the ray correctly?

A light rope is joined to a heavy rope, and the ropes are stretched in a straight line. Waves travel more slowly on the heavy rope than on the light rope. An upward pulse travels along the light rope towards the join.

Which row describes the pulse reflected at the join and the pulse transmitted into the heavy rope?

Two pulses of identical shape travel towards each other along a stretched rope. One pulse is upright and the other is inverted. At one instant the pulses overlap exactly and the whole rope is straight.

Which statement about the rope at this instant is correct?

Monochromatic light passes through a single narrow slit and forms a diffraction pattern on a distant screen. The width of the slit is doubled; the light source is unchanged.

Which statements about the new pattern are correct?

I. The central maximum is narrower.

II. The intensity at the centre of the pattern is greater.

III. The secondary maxima are further apart.

Monochromatic light passes through two identical slits, each of width b, whose centres are a distance d apart. The graph shows how the intensity of the light on a distant screen varies with the position y on the screen.

What is d/b?

Light from a mercury lamp contains two lines of wavelength 546.1 nm and 577.0 nm. The light is incident normally on a diffraction grating with 400 lines per mm.

What is the angle between the two lines in the second-order spectrum?

White light containing all wavelengths from 400 nm to 700 nm is incident on a double slit. Point P on the screen is the centre of the third bright fringe from the central fringe for light of wavelength 650 nm.

Which wavelengths in the white light have a minimum of intensity at P?

Two loudspeakers S₁ and S₂ are connected to the same signal generator and emit sound of the same frequency. A listener walks along a line parallel to S₁S₂ and some distance from it, and hears loud and quiet points. An electronic delay is then added so that the sound from S₂ lags the sound from S₁ by one quarter of a period.

Which row describes the loud point nearest to the line through the midpoint of S₁S₂, and the separation of adjacent loud points, after the delay is added?

Straight water waves cross a straight boundary between two regions of a ripple tank. The wavelength is λ₁ in the first region and λ₂ in the second. The ray in the first region makes an angle θ₁ with the normal to the boundary.

What is the angle θ₂ between the ray in the second region and the normal?

In a double-slit experiment with slit separation d, the fringe spacing on the screen is s. The distance from the slits to the screen is not known. The screen is then moved a further distance x away from the slits, and the fringe spacing becomes s′.

What is the wavelength of the light?

Two waves travel in the same direction along a long rope. The graph shows the displacement each wave would produce on its own, at one instant, against position x along the rope.

What is the displacement of the rope at point P at this instant?

A student uses a diffraction grating on a spectrometer to study light from a hydrogen discharge tube. The light is made parallel and falls normally on the grating. A telescope is rotated to each maximum and its angular position is read from a circular scale. Positions to the right of the scale zero are positive and to the left negative.

For the red hydrogen line of wavelength 656.3 nm, the first three orders are found on both sides. The telescope reading for the straight-through beam was not recorded. A violet line is seen in first order only on this table.

A ray box sends a narrow ray of light into the curved face of a semicircular glass block, along a radius, so that it reaches the centre of the flat face and leaves the block into air. The block is placed on a printed polar grid so that the angle of incidence inside the glass, θ₂, can be set precisely. The angle of refraction in air, θ₁, is read from the grid to ±1°.

Student X suggests that θ₁/θ₂ is constant. Student Y suggests that sin θ₁/sin θ₂ is constant.

Light from a laser passes through an adjustable slit and forms a diffraction pattern on a screen 1.500 m away. The slit width is set with a screw and read from a scale as b_s. The width w of the central maximum on the screen (between the first minima on either side) is measured with a ruler.

For small angles the slit width b is related to w by w = 2λD/b. The student plots b_s against 1/w. The graph shows the data and the line of best fit.

A laser beam falls on a double slit of separation 0.400 mm and an interference pattern forms on a screen. The student moves the screen to five positions and measures the distance D from the screen to the front edge of the stand that holds the slide. For each position the student measures the distance across 10 fringe spacings with a ruler; each measurement has an uncertainty of ±0.5 mm.

The graph shows the fringe spacing s against D. The line of best fit has been extended to the D axis.

Short pulses of light from a laser diode are sent into one end of a reel of optical fibre. A detector at the other end is connected to an oscilloscope, which displays the time t between the electrical trigger signal and the arrival of the light pulse. The measurement is repeated for reels of different length L. The time includes a fixed delay in the electronics and connecting cables. Each value of t is uncertain by ±2 ns.

The graph shows t against L with the line of best fit.

A student estimates the Planck constant using five light-emitting diodes (LEDs). Each LED in turn illuminates a double slit of separation 0.250 mm, and the distance across 10 fringe spacings is measured on a screen 1.800 m away. The wavelength λ is calculated from the fringe spacing. The student then finds the threshold voltage V_th, the smallest potential difference at which the LED just begins to emit light.

The model is eV_th = hc/λ, so a graph of V_th against 1/λ should be a straight line through the origin. The graph shows the data (note the false origins).

A food scientist builds a refractometer to find the sugar concentration of fruit juices. A laser beam passes along a radius of a semicircular dish holding the solution and meets the flat face at its centre. The angle of incidence is increased until the refracted ray just skims along the flat face; this is the critical angle c, measured to ±0.2°. The refractive index is then n = 1/sin c.

Solutions of known sugar concentration C (percentage by mass) are used to plot the calibration graph of n against C.

In an electron-diffraction tube, electrons accelerated from rest through a potential difference V pass through a thin layer of graphite and form bright rings on a fluorescent screen. The radius r of the inner ring is measured with vernier calipers. For this ring the geometry of the tube gives r/L = λ/d, where L = 0.130 m and d is a spacing between planes of carbon atoms.

The graph shows r against V^−1/2 with the line of best fit.

A student investigates how the fringe spacing s in a double-slit interference pattern depends on the slit separation d. A slide carrying six double slits of known separation is placed in the beam of a red laser, and the pattern is viewed on a screen at a fixed distance D = 1.500 m from the slide. For each double slit the student measures the distance across ten fringe spacings, 10s, with a ruler. Each value of 10s has an uncertainty of ±0.5 mm.

The graph shows s against 1/d with the line of best fit.

Two loudspeakers, d = 2.00 m apart, are connected to the same signal generator and emit sound in phase. A microphone is moved along a line parallel to the line joining the speakers and D = 4.00 m from it. For each frequency f of the generator, a student measures the distance w between the second quiet point on one side of the central loud point and the second quiet point on the other side. Each value of w has an uncertainty of ±0.02 m.

The fringe separation is given by s = vD/(fd), where v is the speed of sound. The graph shows w against 1/f with error bars and the line of best fit.

A green laser of wavelength 532 nm is directed normally at a diffraction grating. The spots of the diffraction pattern fall on a flat wall parallel to the grating, at a distance L = 0.400 m from it. Because the position of the central spot is hard to mark, for each order n the student measures the distance 2x between the two spots of that order on opposite sides of the centre.

The student calculates sin θ for each order, where θ is the angle between the straight-through direction and the beam of order n. The graph shows sin θ against n.

In a modern version of the double-slit experiment, electrons are accelerated from rest through a potential difference of 600 V and then pass through two slits cut in a thin membrane. Each slit has width 75 nm and the centres of the slits are 300 nm apart. The electrons are detected on a screen 1.50 m beyond the slits.

A geostationary communications satellite transmits to the Earth at a frequency of 12.0 GHz from a circular dish of diameter 2.40 m. The angle between the centre of the beam and its first minimum can be estimated from the single-slit result θ = λ/b, where b is the diameter of the dish.

Light from a laser diode passes through a double slit and falls on a screen 1.60 m away. A light sensor is moved across the screen, and the graph shows the variation of the intensity I it records with position y on the screen. The centres of the slits are 0.180 mm apart.

A diver at depth h below the calm surface of a swimming pool looks upwards. She sees the whole sky above the pool compressed into a bright circle (a "window") on the surface directly above her. Outside this circle the surface looks like a mirror. The refractive index of the water is 1.33.

The data on a DVD are stored along a spiral track. Adjacent turns of the track are a distance d apart, so the disc acts as a reflection grating. A laser beam of wavelength 650 nm is directed normally onto the disc, and the first-order reflected beams make an angle of 61.4° with the incident beam. The grating equation nλ = d sin θ applies.

A step-index optical fibre of length 2.00 km has a core of refractive index 1.480 and a cladding of refractive index 1.460. Pulses of infrared radiation of wavelength 1310 nm are sent along it. Some of the radiation in a pulse travels along the axis of the core, and some zig-zags along the core, meeting the core–cladding boundary at the critical angle.

Two radio transmitters, 1.50 km apart, broadcast the same programme in phase at a frequency of 96.0 MHz. A straight road runs parallel to the line joining the transmitters at a perpendicular distance of 12.0 km from it. A driver on the road notices that the radio signal fades and recovers regularly.

The graph shows how the speed of long water waves depends on the depth of the water. Ocean swell of period 8.0 s travels over a sea bed where the water depth changes suddenly from 4.0 m to 1.0 m along a straight underwater ledge.