Explain how to get a reasonable estimate for 11/12 ÷ 1/4

A)  θ = 3.36 10⁻⁴ rad

B) y = 8.4 10⁻⁵ m

C)  θ = 3.36 10⁻⁴ rad

D) the correct answer is 1 the value found is close to the experimental one

E)  the size of the cells is the one that most limits the minimum size of the object that we can see.  

Explanation:

A) The Rayleigh criterion determines what is the size of two objects that can be resolved due to diffraction, it establishes that the bodies are resolved if the maximum diffraction of one coincides with the first minimum of diffraction of the other, based on this it is get

for a slit      θ = λ / D

for a circular aperture, solving in polar coordinates gives the expression

                  θ = 1.22 λ / D

in our case the diameter of the pupil is D = 2.00 mm = 0.002 m                    

they tell us to use lam = 550 nm

              θ = 1.22 550 10⁻⁹ / 0.002

              θ = 3.36 10⁻⁴ rad

The angle that the object covers is

           tan θ' = y / x

           θ' = tan⁻¹ (50 10⁻³/25 10⁻²)

           θ' = 0.197

Since the angle supported by the object is greater than the minimum angle, it is resolved or is visible

B) The smallest size of the visible or resolved object

           y = x tan θ

           y = 0.25 tan 3.36 10⁻⁴

           y = 8.4 10⁻⁵ m

C) θ = 3.36 10⁻⁴ rad

D)  θ_exp= 1 min

we reduce to degre

     θ_exp= 1 min (1 ° / 60 min) = 1/60 °

we reduce to radians

     θ_exp  = 1/60 ° (π rad / 180 °)

     θ_exp = 2.9 10⁻⁴ rad

When comparing these two values ​​the order of magnitude is the same, even though the real value is a little smaller.

the correct answer is 1 the value found is close to the experimental one

E) The angle supported by the size of the retinal cells is 0.197 rad calculated in part A

the angle of resolution by diffraction is 3.36 10⁻⁴ radians

When comparing these two values ​​we see that the size of the cells is the one that most limits the minimum size of the object that we can see.