A Thin Flm Of ata Halliday, Fundamentals of Physics, 10e (a) How far from grains

Question

A Thin Flm Of ata Halliday, Fundamentals of Physics, 10e (a) How far from grains of red sand must you be to position yourself just at the limit of resolving the grains if your pupil diameter is 1.7 mm, the grains are spherical with radus 59 um, and the light from the grains has wavelength 640 nm? (b) If the grains were blue and the light from them had wavelength 400 nm, would the answer to (a) be larger or (a) Number Units Open Show Work Click if you would like to Show Work for this question: Study

Explanation / Answer

Call distance L. Theta = diameter/L = 2 x 59x10E-6/ L = 1.18E-4/L radians

sin(theta) =1.22lambda/aperture

For small angles, sin(theta) = theta so

1.18E-4/L = 1.22 x 640E-9 / 1.7E-3

L= 0.257 m

(b)If the wavelength were smaller, L would be latger (you would be dividing by 400. not 640).

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