Question

Suppose that aliens from a planet orbiting Betelgeuse have eyes similar to human eyes, except that the diameter of their pupils is 0.5m rather than 0.007m for humans. How far from Betelgeuse must they travel before it is just visible to them?

Answer 1

Answer:

Answered

Explanation:

The data given in the problem

Diameter of a human pupil=0.007 m=7 mm

Diameter of alien pupil=0.5=500 mm

Here we have to calculate the minimum distance at which the alien can see Betelgeuse i.e. the focal length (or the working distance). For this calculation we assume the eye to be a spherical lens.

The focal length and diameter of the lens are related by the formula $F=\frac{r}{2}$ Where r is radius of curvature i.e. d/2

Therefore for the alien, focal length=$F=\frac{25}{2}=12.5mm=0.0125F=\frac{25}{2}$=12.5mm=0.0125