1) Two stars are photographed utilizing a telescope with a circular aperture of
ID: 1609914 • Letter: 1
Question
1) Two stars are photographed utilizing a telescope with a circular aperture of diameter of 2.32 m and light with a wavelength of 535 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 1.17 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 14.2 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
From the Raley criterian formula
theta = 1.22 lamda/D
for small angles theta = tan theta = d/L
d/L = 1.22 lamda/D
d= 1.22 lamda L/D
= 1.22 ( 535* 10^-9)( 10^22 m/2.32
=281.33* 10^13 m
(2)
d= 1.22 lamda L/D
lamda = dD/1.22 L
=1.17 ( 7* 10^-3)/1.22 ( 14.2 * 10^3 m)
=472.75 nm
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