Phase and phase difference

The diagram shows how displacement varies with distance for two waves, X and Y, at a particular instant. The waves are travelling to the right.

Which of the following statements describes the phase relationship between the two waves?

Scientists can analyse light from stars that has passed through a diffraction grating.

*(a) Explain the pattern produced when a mixture of blue and red light, from the same source, passes through a diffraction grating.

Light interacts with atoms as it passes through the atmosphere of the star.

Explain how this leads to the formation of the dark lines within the spectrum.

The surface temperature of the star is 5800 K.

On the axes below, sketch a graph of the intensity of radiation against the wavelength of that radiation for this star.

This star is a main sequence star.

Explain why main sequence stars do not collapse due to gravitational forces.

A simple astronomical refracting telescope consists of two converging lenses. Light from a star is brought to a focus by the objective lens and then viewed through an eyepiece lens as shown.

In the arrangement shown, the final image is formed at infinity.

Explain why the separation of the objective and eyepiece lenses is equal to the sum of their focal lengths.

State why the final image is inverted.

Glass lenses used for optical instruments often have an anti-reflective coating. The coating is a thin layer of a transparent substance with refractive index n_c. Light is reflected from the coating surface and from the lens surface as shown. The reflected light interferes destructively.

When a single-layer coating is used, the coating thickness is chosen to eliminate reflections for green light, which is in the middle of the visible spectrum.

Calculate the minimum thickness d of the coating required for the reflection of green light to be eliminated.

frequency of green light = 6.00 10¹⁴Hz

State why white light reflected from coated lenses is seen as purple.

The mouse repeller produces ultrasound of frequency 26.0 kHz.

A method to determine the wavelength of light using a converging lens was first proposed by Sir Isaac Newton.

A converging lens is placed on a plane glass plate. The lens is illuminated from above with a parallel beam of monochromatic light, as shown.

Some of the light is reflected from the upper surface of the lower glass plate and some from the lower surface of the lens. Interference between these two reflected waves produces circular fringes. The pattern is viewed through a microscope.

The diameter D of each circular fringe, numbered N from the centre, is measured using the microscope. The data obtained from such an experiment is shown.

The relationship between N and D is of the form D = pN^q where p and q are constants.

Determine p and q for this data using a graphical method. Use the additional columns for your processed data.

The table below shows the readings from which the diameter of the first dark circle was calculated.

Use these readings to estimate the percentage uncertainty in the diameter due to the resolution of the instrument.

State why the actual percentage uncertainty would have been greater than the value calculated in (b)(i).

When considering the principles of this experiment, a student suggests that interference fringes would only be produced with monochromatic light. This is because interference requires coherent light waves.

Discuss the validity of the student’s suggestion.

In 2016 scientists at the Laser Interferometer Gravitational‑Wave Observatory (LIGO) announced that gravitational waves had been detected.

The signal they detected is shown on the graph.

Gravitational waves travel at the speed of light.

Determine the mean wavelength of the waves detected between 0.30 s and 0.35 s on the graph.

Gravitational waves alternately compress and stretch matter by very small amounts as they pass through.

The LIGO detector has two arms, at 90° to each other, each 4 km long. As a gravitational wave passes the detector, the arms change length. The detector continuously compares the lengths of the two arms.

An article states that ‘the maximum change in the 4 km length of the arm is about 0.001 times the diameter of a proton’.

Determine whether this statement applies to the gravitational wave shown in the graph.

diameter of proton = 8.810^–16m

In the LIGO detector, any change in the lengths of the arms is detected using a laser beam and photodetector.

The laser beam is split into two at B, one beam travelling to one mirror and the other beam travelling to the other mirror. After reflection at the mirrors, the beams are recombined at B and reach the photodetector. The photodetector measures the intensity of the incident light.

The system is arranged so that when no gravitational waves are present, the beams have a path difference of half a wavelength at the photodetector.

Explain how the photodetector detects very small changes in the length of one arm, when the other arm stays the same length.

The system could be arranged so that when no gravitational waves are present, the beams have zero path difference at the photodetector.

Explain whether using an initial path difference of half a wavelength is a more sensitive way of detecting changes in length than having an initial path difference of zero.