Q62P
Question
.. BIO Resolution of the Eye. The maximum resolution of the eye depends on the diameter of the opening of the pupil (a diffraction effect) and the size of the retinal cells. The size of the retinal cells (about in diameter) limits the size of an
object at the near point (25 cm) of the eye to a height of about . (To get a reasonable estimate without having to go through complicated calculations, we shall ignore the effect of the fluid in the eye.) (a) Given that the diameter of the human pupil is about , does the Rayleigh criterion allow us to resolve a tall object at from the eye with light of wavelength (b) According to the Rayleigh criterion, what is the shortest object we could resolve at the near point with light of wavelength ? (c) What angle would the object in part (b) subtend at the eye? Express your answer in minutes , and compare it with the experimental value of about 1 min. (d) Which effect is more important in limiting the resolution of our eyes: diffraction or the size of the retinal cells?
Step-by-Step Solution
Verifiedthe answer is No
the shortest object we could resolve is
the angle of an object is 0.019
Diffraction effect is limiting the resolution of eyes
IDENTIFY and SET UP:
This problem uses the ideas about circular diffraction and resolving pOWer of a human eye. In part (a) We use Eq- (36.17) (the Rayleigh criterion) to ?nd the angular separation OR of the shortest object the human pupil (With a diameter )
could resolve at-tall object at the near point Would subtend an angle of 0 =
at the eye. Compare the value of 0R to that of 0 to anSWer part (a)- In part (b), We use
the geometrical relationship 10 = L911 to ?nd the size 20 of the shortest object We could resolve at (the near
point of the eye) with the same wavelength A (according to the Rayleigh criterion)- In part (c) the angle the object in part (b)
would subtend at the eye is 9R We use the relationship to convert the value of 9R from radians to
degrees, and then to minutes (60 min = 1°), before We compare the result with the experimental value of about I min- In part
(d) the anSWer is dependent on the result of part (a).
EXECUTE:
(a) From Eq- (36.17) the angular separation 9R of the shortest object the human pupil could resolve is
which is greater than the value (the angle subtended by the 50-pm-tall object and the near point of the
eye)- Hence, the Rayleigh criterion doesn’ t allow us to resolve a 50-pm-tall object at the near point (25 cm) of the eye With
light of wavelength 550 nm-
Therefore the answer is No
(b) The shortest object We could resolve at the 25-cm near point with A = 550 nm has the size of
Therefore the shortest object we colud resolve is
(c) We have seen in part (b) w = L03 for the size of the shortest object we could resolve at the near point of the eye- It
follows that is the angle this object would subtend at the eye- Since rad is equivalent to 180°, the value
in degrees is
which is equal to 1.] in minutes (1° = 60 min)- We see the result is very close to the experimental value of about 1 min-
Therefore the angle of an object is 0.019
(d) We have seen in part (a) how the human pupil is not capable of resolving a 50-pm-tall object at the 25-cm near point (at = 550 nm), which is the size of an object limited by the size of retinal cells- Hence, We see the diffraction effect (related to
the eye's pupil) is more important in limiting the resolution of our eyes than the size of the retinal cells.
EVALUATE:
According to the Rayleigh criterion, our eyes can resolve a 50-pm-tall object at the 25-cm near point of the eye (this
corresponds to an angular resolution of) at light with wavelength= 550 nm when the opening of the
pupil reaches to in diameter.
Therefore Diffraction effect is limiting the resolution of eyes