7. Image formation. Optics of the eye.

Question 1

Define accommodation and give the according formulas for:

• optical power
• accomodation power

Answer 1

Accommodation:

adaption of the eye’s optical power, achieved by changing the curvature of the lens → **sharp vision **

• ciliary muscles contract to focus on close objects

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Optical power: D = n_air/o + n’_{vitreous humor}/i

Accomodation power: ΔD = 1/o_r - 1/o_p

Question 2

Describe 3 refraction problems of the eye and with what type of lens they can be corrected

Answer 2

Myopia (nearsightedness):

• elongated eyeball → focused in front of retina
• see well close objects → o_r < ∞
• corrected with divergent (-) lens

Hyperopia (farsightedness):

• shortened eyeball → focused behind retina
• see well far objects
• corrected with convergent (+) lens
• corrected with bifocal lens (2 different f)

Presbyopia (effect of aging of the eye):

• loss of eleasticity of lens → remains flat
• aging → o_p recedes → ΔD decreases
• corrected with convergent (+) lens
• be corrected with bifocal lens (2 different f)

Question 3

Describe the biological limit of resolution. What is the formula for the visual acuity?

Answer 3

Biological limit of resolution:

Biological limiting angle of view determined by receptor cell density ~ α=0.8’ (one inactivated between two activated, otherwise detail cannot be perceived)

Visual acuity:

Ratio of normal limiting angle of view Φ to actual limiting angle α of view in percent

• acuity = 1’ / α (‘) * 100%

Question 4

Explain the diffraction limit of resolution refering to the Rayleigh criterion. From what other formula was it derived?

Answer 4

Diffraction limit of resolution:

objects may be resolved if their corresponding Airy disks do not overlap

It is derived from the Abbés formula

α_D = 1.22 * λ/d

• d = diameter of lens’ aperture

⇒ α=0.6’

Question 5

Explain the image formation of the eye refering to the reduced eye model. What is it?

Name its features. How can the size of the image be determined?

Answer 5

Reduced model of the eye:

• used to illustrate image formation of the eye
• homogeneous body possessing only one single refracting surface created.

Features:

• index of refraction n = 1.34
• lens curvature r = 5.1mm
• distance of nodal point (=center of curvature) K to yellow spot = 17mm

Formula for size of the image: a’ = i * a/x