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It is claimed that some professional baseball players can see which way the ball is spinning as it travels toward home plate. One way to judge this claim is to estimate the distance at which a batter can first hope to resolve two points on opposite sides of a baseball, which has a diameter of 0.0738 m.

(a) Estimate this distance, assuming that the pupil of the eye has a diameter of 2.00 mm and the wavelength of the light is 550 nm in vacuum.
(b) Considering that the distance between the pitcher’s mound and home plate is 18.4 m, can you rule out the claim based on your answer to part (a)?

Respuesta :

Manetho

Answer:

a)220 m

b)No

Explanation:

The minimum angular separation is given by the formula

[tex]\theta_{min}= \frac{1.222\lambda}{D}[/tex]

here λ= 550 nm and D= 2 mm

[tex]\theta_{min}= \frac{1.222\times550\times10^{-9}}{2\times10^{-3}}[/tex]

θmin= 3.4×10^{-4} rad

using radian measure we can also express θmin as follows

and their obtain a value for distance L

[tex]\theta_{min}= \frac{y}{L}[/tex]

or

[tex]L= \frac{y}{\theta_{min}}[/tex]

[tex]L= \frac{0.0738}{3.4\times10^{-4}}[/tex]

=220 m

b) SInce the distance is 220 m at which the two points can be separated is greater than the 18.4 m the distance between the pitcher's mound and the home plate cannot rule out the claim. Hence the answer is NO.

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