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

Question

a) Two stars are photographed utilizing a telescope with a circular aperture of diameter of 2.41 m and light with a wavelength of 509 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 =

b) A car passes you on the highway and you notice the taillights of the car are 1.21 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 14 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)?

=

Please Help!! Thank You!!

Explanation / Answer

Given that

The circular aperature of diameter (d) =2.41m

The separation between the two stars be (D) =1022m

The light of wavelength is(lamda) =509 nm =509*10-9m

Now from the Rayleigh criterion the minimum angular separation is given by

sinthetamin =1.22*lamda/d ( where d is the diameter of the circular aperature)

sintheamin =1.22*509*10-9m/2.41m =2.576*10-7

Now we can also write

sinthemin =x/D

Then x =D*sintheamin =(1022m)(2.576*10-7) =2.633*10-4m

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