The same telescope is used to observe a different galaxy at a distance of 3.8 × 1027 m from Earth. The astronomer wishes to resolve two stars with a separation of 2.3 × 1022 m.
(c)
Determine whether the telescope is able to resolve the light from the stars.
The astronomer working with the telescope wishes to determine if sodium is present in the stars. To do this they use a diffraction grating to split the light from the star.
The two wavelengths of light they wish to resolve are 589.0 nm and 589.6 nm.
(d)
Determine the resolving power of the diffraction grating required to resolve these wavelengths.
A second monochromatic light source of 630 nm is placed alongside the original monochromatic light source of wavelength 610 nm. The width of the beam of light from these sources is 2.0 mm.
(c)
(i)
Calculate the resolving power of the diffraction grating.
[3]
(ii)
Calculate the minimum number of lines per mm required to resolve the two light sources for the second order maximum.
A binary star system is observed using a telescope with a circular lens. The images of the two stars can just be resolved according to the Rayleigh criterion.
(a)
Outline what is meant by the statement “just resolved according to the Rayleigh criterion” in this context.
The circular lens has a diameter of 4 mm. The distance from the Earth to the binary star system is 6.2 × 1016 m, and the average wavelength of light emitted by the stars is 470 nm.
The telescope is directed at a different area of the sky to detect further binary systems, using a larger diameter lens. A potential binary system with the same average wavelength of light, and the same separation between the stars is detected at 9.1 × 1018 m distance from the earth.
The light from the binary system is passed through a diffraction grating with 430 lines per mm. The difference in wavelength between the two stars is 1.3 nm.
(d)
(i)
Determine the resolving power of the diffraction grating
[1]
(ii)
Hence calculate the width of the beam of light received from the stars to produce resolution of the two stars in the 3rd order spectrum
A man stands on an airstrip at night as a car approaches him. His pupils have a diameter of 3.2 mm and the wavelength of the light is 490 nm. He can just resolve the light from the headlights of the car into two distinct points.
The car is moving at 20 m s−1 and the headlights are 1.6 m apart.
(a)
(i)
Calculate the Rayleigh criterion for this situation.
[1]
(ii)
Determine the time the man has to leave the airstrip before he is hit by the car.
Draw a labelled sketch of the variation of intensity of light with angle, θ, as it falls on the man's retina at the point where the two headlights can just be resolved.
Hovering above the airstrip is a helicopter on which the man can just resolve two light sources. The helicopter is hovering at 25% of the distance at which the car lights were able to be resolved, and the separation between the lights is 0.45 m. The pupil diameter of the man remains unchanged.
(c)
Determine the wavelength of the light emitted by the helicopter's lights.
The man is holding blue lights in each hand to guide the helicopter to a safe landing. He switches to using red lights whilst maintaining the same separation.
(d)
Explain the effect on how the helicopter pilot observes the lights
