Two stars are photographed utilizing a telescope with a circular aperture of dia

Question

Two stars are photographed utilizing a telescope with a circular aperture of diameter of 2.33 m and light with a wavelength of 503 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 1.25 m apart. Assume that the pupils of your eyes have a diameter of 7 mm and index of refraction of 1.36. Given that the car is 13.7 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

given data
diameter =2.33 m
wave length = 503 nm
distance =10^22m

Minimum angular resolution (min) given by the Rayleigh criterion ..
sin (min) = 1.22 /a where (a = lens width)

sin (min) = 1.22 *(503*10^-9) / 2.33
sin (min) = 2.633*10^-7

Applying (min) to sources separated by distance x at 10^22m
sin (min) = x / 10^22

2.633*10^-7 *10^22 =x

2.633*10^15 m =x

2)

given data
distance = 1.25m
dimeter=7mm
index of refraction=1.36
car distance = 13.7km

sin (min) = 1.22 /a
Within eye ' = /n .. (= wavelength in air, n=ref.index 1.36)

sin (min) = 1.22 '/ (7*10^-3m) = 1.22 / (1.36(7*10^-3m)).
sin (min) = 128

Outside the eye..
sin (min) = source sep. / distance = 1.25m / (13.7*10^3m) = 9.12*10^-5

sin (min) = 9.12*10^-5 = 128

= 7.125*10^-7 =712.5nm

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