A painter employed a method of painting with small dots of color placed close altogether on canvas. From sufficiently far away, the dots can’t be differentiated and the painting looks normal in appearance.
(i) When the dots on the painting are separated through 1.5 mm and the painting is observed beneath light of 550 nm wavelength with eyes having a pupil diameter of 2 mm, determine the minimum distance you should stand from the painting so that the individual dots can’t be resolved.
(ii) Beneath the conditions of part (i), what would be the distance among the images of dots on the retina of the eye, 2.0 cm behind the lens of the eye?
(iii) When a small scaled copy of a painting is made that is 100-fold smaller in size, the dots would be anticipated to be spaced just 0.015 mm, too small to be resolved with the naked eye. By using a compound microscope having a 10X eyepiece and 17 cm tube length, determine what maximum focal length of objective lens would be required to test the scaled copy for authenticity (meaning that the painting is made from small dots, instead of continuous color).