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 2.34 m and light with a wavelength of 473 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 1.14 m apart. Assume that the pupils of your eyes have a diameter of 6.7 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 that

lambda = 473 nm

diameter of aperture a = 2.34 m

d = 10^22 m

from rayleigh criteria

minimum angular resolution

sin(theta) = 1.22 * lambda / a

sin (theta) = source sepration / distance

source sepration x = 1.22 * lambda * d / a = 1.22*473*10^(-9) * 10^22 / 2.34

x = 2.46*10^15 m

(b)

given that

diameter a = 6.7 mm = 6.7*10(-3) m

d = 13.7 km

x = 1.14 m

n = index of refraction = 1.36

lambda' = lambda / n

where lambda' = wavelength in medium & lambda = wavelength in vaccum

sin (theta) = source sepration / distance = 1.22 * lambda' / a

lambda' = 1.14*6.7*10^(-3) / 1.22*13.7*10^3

lambda' = 0.4569*10^(-6) m

lambda = lambda'*n = 0.4569*10^(-6) * 1.36

lambda = 621 nm

answer

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