1) Two stars are photographed utilizing a telescope with a circular aperture of
ID: 1502411 • Letter: 1
Question
1)
Two stars are photographed utilizing a telescope with a circular aperture of diameter of 2.46 m and light with a wavelength of 534 nm. If both stars are 1022 m from us, what is their minimum separation so that we can recognize them as two stars (instead of just one)?
d =
m
2)
A car passes you on the highway and you notice the taillights of the car are 1.26 m apart. Assume that the pupils of your eyes have a diameter of 7.3 mm and index of refraction of 1.36. Given that the car is 14.3 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)?
=
nm
Explanation / Answer
I will assume 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 (534^-9m) / 2.46m
sin (min) = 2.64*10^-7
Applying (min) to sources separated by distance x at 1.0^23m
sin (min) = x / 1.0*10^23 = 2.64*10^-7m .. .. x = 2.64*10^16 m
[if D = 1.0^22m .. .. x = 2.64^15 m]
b) sin (min) = 1.22 /a
Within eye ' = /n .. (= wavelength in air, n=ref.index 1.36)
sin (min) = 1.22 '/ (7.3^-3m) = 1.22 / 1.36(7.3^-3m) ..
sin (min) = 123
Outside the eye..
sin (min) = source sep. / distance = 1.26m / 14.3*10^3m = 8.811^-5
sin (min) = 8.811^-5 = 123 .. .. = 7.163^-7m .. (716 nm)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.