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DIFFRACTION IN EYES, MICROSCOPES, AND ULTRASOUND READING 1 Two point sources can be resolved by an optical system if the corresponding diffraction patterns are sufficiently small or sufficiently separated. By definition, the "minimum resolvable separation" is when the maximum of the diffraction pattern of one source falls on the first minimum of the diffraction pattern of the other. For a circular aperture, this distance in angular measure (radians) is given by: ? = 1.22?m / d where ?m is the wavelength of light visualized, d is the diameter of the aperture, and ? is the angular separation. The wavelength of light in a material ?m is smaller than the wavelength in vacuum ?o by the ratio ?m = ?o / n, where n is the index of refraction. So the formula can be generalized to: ? = 1.22?o / (n * d) This formula determines the diffraction-limited resolving power of an aperture with diameter d. This angular separation can be converted to an approximate linear separation, D, at the retina using: ? = D / 0.025 where 0.025 is the corneal-retinal distance in meters. (Note: The lab manual has a typo and should have D in this last equation. D is not the same as d.) Limitations of the human eye What is the linear separation D at the retina? The minimum diameter of the pupil is about 2 mm, the eye is most sensitive to wavelengths of about 500 nm (air), the index of refraction of the aqueous humor is n = 1.33, and the distance between the cornea and retina is about 2.5 cm. __________ micrometers (This is a very small distance - approximately 1/100 the size of a period.)

DIFFRACTION IN EYES, MICROSCOPES, AND ULTRASOUND

READING 1

Two point sources can be resolved by an optical system if the corresponding diffraction
patterns are sufficiently small or sufficiently separated. By definition, the "minimum
resolvable separation" is when the maximum of the diffraction pattern of one source falls
on the first minimum of the diffraction pattern of the other. For a circular aperture, this
distance in angular measure (radians) is given by:

? = 1.22?m / d

where ?m is the wavelength of light visualized, d is the diameter of the aperture, and ? is
the angular separation. The wavelength of light in a material ?m is smaller than the
wavelength in vacuum ?o by the ratio ?m = ?o / n, where n is the index of refraction. So the
formula can be generalized to:

? = 1.22?o / (n * d)

This formula determines the diffraction-limited resolving power of an aperture with
diameter d. This angular separation can be converted to an approximate linear separation,
D, at the retina using:

? = D / 0.025

where 0.025 is the corneal-retinal distance in meters. (Note: The lab manual has a typo
and should have D in this last equation. D is not the same as d.)

Limitations of the human eye

What is the linear separation D at the retina? The minimum diameter of the pupil is about
2 mm, the eye is most sensitive to wavelengths of about 500 nm (air), the index of
refraction of the aqueous humor is n = 1.33, and the distance between the cornea and
retina is about 2.5 cm.

__________ micrometers

(This is a very small distance - approximately 1/100 the size of a period.)

$DIFFRACTION IN EYES, MICROSCOPES, AND ULTRASOUND READING 1 Two point sources can be resolved by an optical system if the corresponding diffraction patterns are sufficiently small or sufficiently separated. By definition, the "minimum resolvable separation" is when the maximum of the diffraction pattern of one source falls on the first minimum of the diffraction pattern of the other. For a circular aperture, this distance in angular measure (radians) is given by: ? = 1.22?m / d where ?m is the wavelength of light visualized, d is the diameter of the aperture, and ? is the angular separation. The wavelength of light in a material ?m is smaller than the wavelength in vacuum ?o by the ratio ?m = ?o / n, where n is the index of refraction. So the formula can be generalized to: ? = 1.22?o / (n * d) This formula determines the diffraction-limited resolving power of an aperture with diameter d. This angular separation can be converted to an approximate linear separation, D, at the retina using: ? = D / 0.025 where 0.025 is the corneal-retinal distance in meters. (Note: The lab manual has a typo and should have D in this last equation. D is not the same as d.) Limitations of the human eye What is the linear separation D at the retina? The minimum diameter of the pupil is about 2 mm, the eye is most sensitive to wavelengths of about 500 nm (air), the index of refraction of the aqueous humor is n = 1.33, and the distance between the cornea and retina is about 2.5 cm. micrometers (This is a very small distance - approximately 1/100 the size of a period.)$

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