1.) Two stars are photographed utilizing a telescope with a circular aperture of
ID: 1501051 • Letter: 1
Question
1.) Two stars are photographed utilizing a telescope with a circular aperture of diameter of 2.38 m and light with a wavelength of 491 nm. If both stars are 10^22 m from us, what is their minimum separation so that we can recognize them as two stars (instead of just one)?
d =
2) A car passes you on the highway and you notice the taillights of the car are 1.18 m apart. Assume that the pupils of your eyes have a diameter of 6.9 mm and index of refraction of 1.36. Given that the car is 13.9 km away when the taillights appear to merge into a single spot of light because of the effects of diffraction, what wavelength of light does the car emit from its taillights (what would the wavelength be in vacuum)?
=
Explanation / Answer
a)
D = 10^22 = 1.0^23m
Minimum angular resolution (min) given by the Rayleigh criterion ..
sin (min) = 1.22 /a .. (a = lens width)
sin (min) = 1.22 (491^-9m) / 2.38m
sin (min) = 2.5168^-7
Applying (min) to sources separated by distance x at 1.0^23m
sin (min) = x / 1.0^23 = 2.5168^-7m .. .. x = 2.52* 10^16 m
b) sin (min) = 1.22 /a
Within eye ' = /n .. (= wavelength in air, n=ref.index 1.36)
sin (min) = 1.22 '/ (6.90^-3m) = 1.22 / 1.36(6.90^-3m) ..
sin (min) = 130
Outside the eye..
sin (min) = source sep. / distance = 1.18m / 13.9^3m = 8.49^-5
sin (min) = 8.49^-5 = 130 .. .. = 6.53^-7m .. (653 nm)
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