OCR A-Level Physics: Waves and Optics

Light from a small filament lamp is unpolarised. It is passed through a polarising filter (a polaroid), and then a second identical filter is placed in the beam behind the first. The second filter is slowly rotated through a full turn while the brightness of the light emerging from it is observed.

Explain what is meant by a polarised wave, how the arrangement above produces and then analyses plane-polarised light, and how this experiment provides evidence that light is a transverse wave. In your answer you should refer to the plane of oscillation, what happens to the transmitted brightness as the second filter is rotated, and why the same observation would be impossible for a longitudinal wave such as sound.

(6 marks)

In a school laboratory, monochromatic laser light is directed normally at a diffraction grating. The angles at which the first few bright maxima appear, measured from the straight-through (zero-order) direction, are recorded:

Order, $n$n	Angle from centre, $\theta$θ / °
1	18.9
2	41.1

The grating is engraved with 600 lines per millimetre.

(a) Calculate the grating spacing $d$d, the distance between the centres of adjacent slits. (2 marks)

(b) Use the first-order reading to calculate the wavelength of the laser light. (2 marks)

(c) Determine the highest order of maximum that this grating can produce with this light. (2 marks)

A student investigates Young's double-slit experiment using a laser. The two slits are a fixed distance apart and the screen is 2.40 m from the slits. To improve accuracy the student measures the distance across several fringe spacings and divides, recording the distance spanned by 10 fringe spacings:

Quantity	Value
Slit separation, $a$a	0.30 mm
Slit-to-screen distance, $D$D	2.40 m
Width of 10 fringe spacings	25.6 mm

The fringe spacing $x$x is related to the wavelength by $\lambda = \dfrac{ax}{D}$λ=Dax​.

(a) Use the data to determine the wavelength of the laser light. (3 marks)

(b) The student now replaces the laser with one that emits shorter-wavelength light, keeping $a$a and $D$D the same. State and explain the effect on the fringe spacing seen on the screen. (2 marks)

A beam of unpolarised light of intensity $I_{0}$I0​ is shone through a stack of three polarising filters arranged one behind the other. Looking along the beam, the transmission axis of the second filter is at 30° to that of the first, and the transmission axis of the third filter is at a further 40° beyond the second (so it is at 70° to the first).

Malus's law for plane-polarised light incident on a filter is $I = I_{0}\cos^2\theta$I=I0​cos2θ.

(a) State the intensity of the light, as a fraction of $I_{0}$I0​, immediately after the first filter, and explain your answer. (1 mark)

(b) Calculate the intensity emerging from the third filter, as a fraction of the original $I_{0}$I0​. (4 marks)

A step-index optical fibre has a glass core of refractive index 1.50 surrounded by a cladding of refractive index 1.42. Light rays travel along the core and are kept inside it by total internal reflection at the core-cladding boundary.

(a) Calculate the critical angle for the boundary between the core and the cladding. (3 marks)

(b) A ray strikes the core-cladding boundary at an angle of incidence of 68° (measured from the normal). State, with a reason, whether this ray is totally internally reflected or partly refracted into the cladding. (1 mark)

A stable two-source interference pattern can only be observed when the two sources are coherent.

(a) State what is meant by two sources being coherent. (1 mark)

(b) The wave equation $v = f\lambda$v=fλ links the speed, frequency and wavelength of a progressive wave. Show, by considering the definitions of frequency and wavelength, why this relationship must hold. (2 marks)