Two point sources of light are separated by 4.0 cm. As viewed through a 13 m dia

Question

Two point sources of light are separated by 4.0 cm. As viewed through a 13 m diameterpinhole, what is the maximum distance from which they can beresolved if red light ( = 690 nm) is used? Lred =______cm Two point sources of light are separated by 4.0 cm. As viewed through a 13 m diameterpinhole, what is the maximum distance from which they can beresolved if red light ( = 690 nm) is used? Lred =______cm As viewed through a 13 m diameterpinhole, what is the maximum distance from which they can beresolved if red light ( = 690 nm) is used? Lred =______cm

Explanation / Answer

Using Rayleighs criterion forresolution:     1.22 = Dsin    where D is the diameter of the pinholeand is the angular separation of the sources. So solve for , and then    tan =d / L     where d is the separation of the twosources, and L is the max distance to the sources. For red light:     sin =1.22 * 0.690 / 13 = 0.06475   where I put thewavelength in m     so = 4.577degrees    and     L = d /tan = 4 / tan4.577 = 62.2 cm For violet light:      sin = 1.22 * 0.4/ 10 = 0.0488   where Iput the wavelength in m     so =   2.797 degrees   and     L = d / tan = 4 / tan2.797= 81.87 cm     so =   2.797 degrees   and     L = d / tan = 4 / tan2.797= 81.87 cm

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