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 2.35 m and light with a wavelength of 477 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=

2. A car passes you on the highway and you notice the taillights of the car are 1.15 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

1.
D = 10^22 = 1.0^23m

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

sin (min) = 1.22 (477 x 10^-9m) / 2.35m
sin (min) = 2.476 x 10^-7

Applying (min) to sources separated by distance x at 1.0^23m
sin (min) = x / 1.0^23 = 2.476 x 10^-7m .. ..
x = 2.476 x 10^16 m

2.
sin (min) = 1.22 /a
Within eye ' = /n .. (= wavelength in air, n=ref.index 1.36)

sin (min) = 1.22 '/ (6.7 x 10^-3m) = 1.22 / 1.36(6.7 x 10^-3m) ..
sin (min) = 133.89

Outside the eye..
sin (min) = source sep. / distance = 1.15m / 13.7 x 10^3m = 8.394 x10^-5

sin (min) = 8.394 x10^-5 = 133.89 .. ..
= 6.269x 10^-7m .. (626.9 nm)

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