Answer:
The value is [tex]r = 6557 \ m[/tex]
Explanation:
From the question we are told that
The separation between the light is [tex]s = 1.3 \ m[/tex]
The diameter of the pupil is [tex]d = 4.0 \ mm = 0.004 \ m[/tex]
The wavelength is [tex]\lambda = 650 \ nm = 650 *10^{-9} \ m[/tex]
Generally from Rayleigh criterion can be mathematically represented as
[tex]r = \frac{s * d }{1.22 * \lambda}[/tex]
Here r is the distance you could be from the red taillights of a car and still distinguish them as separate lights
So
[tex]r = \frac{1.3 * 0.004 }{1.22 * 650 *10^{-9}}[/tex]
=> [tex]r = 6557 \ m[/tex]
Using the Rayleigh criterion 6.557 Km away you could be from the red taillights of a car and still distinguish them as separate lights.
Given :
Given that the separation between the light is, s = 1.3 m, the diameter of the pupil is, d = 0.004m, and the wavelength is, [tex]\lambda[/tex] = 650 nm.
The mathematical expression of the Rayleigh criterion is given by:
[tex]r=\dfrac{s\times d }{1.22\times \lambda}[/tex]
Now, put the values of known terms in the above equation.
[tex]r = \dfrac{1.3\times 0.004}{1.22\times 650 \times 10^{-9}}[/tex]
r = 6557 m.
So, using the Rayleigh criterion 6.557 Km away you could be from the red taillights of a car and still distinguish them as separate lights.
For more information, refer to the link given below:
https://brainly.com/question/15610943
