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

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

Expression for limit of resolution

tan = x/d = 1.22 *L / D

Here, x is their minimum separation , d - distance from us, L - wavelength , and D - aperture diameter

Rearrange for x

x = 1.22 *L / D ( d )

Substitute numerical values

x = [ 1.22 ( 534 x 10-9 ) / ( 2.46 m ) ]   ( 1022 m )

x = 2.706 x 10-4 m

Round off the result to 3 significant digits

x = 2.71 x 10-4 m

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