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 2.36 m and light with a wavelength of 475 nm. If both stars are 10^22m from us, what is their minimum separation so that we can recognize them as two stars (instead of just one)? d = 2.456E15 m A car passes you on the highway and you notice the taillights of the car are 1.17 m apart. Assume that the pupils of your eyes have a diameter of 7.4 mm and index of refraction of 1.36. Given that the car is 14.4 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)? lambda = nm

Explanation / Answer

A)

Minimum angular resolution (min) given by the Rayleigh criterion ..

sin (min) = 1.22 /L

sin (min) = (1.22 x 475 x 10^-9 m) / 2.36 m

sin (min) = 2.4555 x 10^-7

Applying (min) to sources separated by distance x at 10 x 10^22

sin (min) = x / (10 x 10^22)

x = 2.4555 x 10^-7 m x 10 x 10^22

x = 2.4555 x 10^15 m

B)

sin (min) = 1.22 /a

Within eye ' = /n

= wavelength in air,

n = ref index

sin (min) = 1.22 '/ (7.4 x 10^-3) = 1.22 / (1.36 x 7.4 x 10^-3m)

sin (min) = 121.22

Outside the eye..

sin (min) = source sep. / distance

= 1.17m / (14.4 x 10^3)

= 8.125 x 10^-5

sin (min) = 8.125 x 10^-5  =  121.22

= 7.237 x 10^-7 m = 670 nm

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