Answer to Question #93209 in Optics for Pratixit Shukla

Question

Eye is most sensitive to 5500Å and the diameter of the pupil is about 2 mm. Find the
angular limit of resolution of eye.

Answer 1

We can find the angular limit of resolution of eye from the formula for the diffraction limit to resolution (also known as Rayleigh criterion):

$$\theta = 1.22 rad \cdot \dfrac{\lambda}{D},$$

here, $\lambda$ is the wavalength of the light, $D$ is the diameter of the pupil.

Then, we get:

$$\theta = 1.22 rad \cdot \dfrac{5500 \text{\AA} \cdot \dfrac{1m}{10^{10} \text{\AA}}}{2 mm \cdot \dfrac{1m}{10^3 mm}} = 3.35 \cdot 10^{-4} rad.$$

Answer:

$\theta = 3.35 \cdot 10^{-4} rad.$