Final answer:
The height of the image of the print on the retina can be calculated using the principles of similar triangles and varies depending on the focal length of the eye. Assuming the focal length of a normal eye is about 2.0 cm, the image height can be found through proportional relation between object and image distances and heights.
Step-by-step explanation:
Calculation of Image Height on the Retina
The question relates to the use of similar triangles to determine the height of an image formed on the retina of the human eye. When a book with print that is 3.50 mm high is held 30.0 cm from the eye, we can calculate the height of the image on the retina using the thin lens equation and understanding the rough estimate of the focal length of the eye, which is approximately 2.0 cm.
Using the Similar Triangles Method
Considering the eye as a simple lens system, the formula
image height / object height = image distance / object distance can be applied to find the height of the print's image on the retina.
Assuming the average focal length is about 2.0 cm (20 mm), and the image is formed on the retina at this distance, we can rearrange this to image height / 3.50 mm = 20 mm / 300 mm. From here we solve for the image height:
image height = (3.50 mm × 20 mm) / 300 mm
After performing the calculation, the result can be analyzed in the context of the human eye's ability to perceive detail, taking into account the size of the rods and cones in the fovea.