It is claimed that some professional baseball players can see which way the ball

Question

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 480 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)?

Explanation / Answer

Apply Raley criterian formula

theta min = 1.22 * lamda/D

theta_ min = 1.22 ( 480* 10^-9)/2* 10^-3)

theta_min = 292.8* 10^-6 rad

The distance between which the points can beresolved is

s = y/ theta_min

= 0.0738/ 292.8* 10^-6 rad

= 252.04 m

(b)

No because  maximum distance at which such two opposite points on the ball can be resolved is way more than the distance of the pitcher form the batter

so, the claim cannot be ruled out.

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