Question

Suppose you are standing on a straight highway and watching a car moving away from you at 25.3 m/s. The air is perfectly clear, and after 1.93 min you see only one taillight. If the diameter of your pupil is 3.4 mm and the index of refraction of your eye is 1.6, estimate the width of the car. (Taillights are red, so use a wavelength of 650 nm.)

Answer 1

Answer:

$\Delta x = 0.68 m$

Explanation:

As we know that limit of resolution of two objects is given as

$\Delta x = L(\frac{1.22 \lambda}{a}$

here we have

L = distance of the car from the eye

$L = vt$

$L = 25.3 \times (1.93 \times 60)$

$L = 2929.74 m$

$\lambda = 650 nm$

$a = 3.4 mm$

now we have

$\Delta x = 2929.74( \frac{1.22 \times 650 \times 10^{-9}}{3.4 \times 10^{-3}})$

$\Delta x = 0.68 m$