Question

Seurat was an impressionist painter who painted using little dots of color--- when an observer steps back away from the paintings, the colors of the dots "blend" in the eye and the observer perceives a continuous picture. Seurat's dots were about 2 mm in diameter, with a separation between the dots also about 2 mm. The color sensitive cells in your retina have a sensitive area with a diameter of about 1?m and you can assume they have a separation (center to center) of about the same distance. For two objects to be perceived as distinct, their images on the retina should be separated by more than that distance on the retina (otherwise, they are both detected by the same cell). The distance from your pupil to your retina is about 1.7 cm.

(A) First, use geometrical optics (ignoring diffraction effects) to determine the distance you would have to stand for the images of the two dots to “blend” together—that is to be detected by the same light sensitive cell. [Hint: assume the “object height” is 2 mm and the “image height” is 1 ?m]

(B) For this part, use the resolution of the eye (35-6) to determine the distance two adjacent dots would have to be from the observer when diffraction effects blur the two dots so the observer cannot distinguish them.

(C) Compare your answers for part (A) and (B) and determine at what distance from the painting you need to stand to see the colors “blend.” Is the blending due to geometrical optics effects or diffraction?

Answer 1

A)

using the linear magnification formula,

-this is the distance you would have to stand for the images of the two dots to “blend” together.

B)

Angular resolution ,

So linear resolution considering difraction ,

So, applying the same formula as in A,

C)

As with the small aperture difraction becomes a noticable effect so we have to consider the minimum distance considering difration. So 9m is the minimum distance where you'll have to stand to see the painting seemlessly.