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