Final answer:
To find the screen distance for a sharp image using a 100 mm focal length lens with the slide placed 103 mm away, we apply the lens formula and determine the screen should be 3,400 mm away. The dimensions of the image for a 24.0 by 36.0 mm slide are calculated using the magnification formula, resulting in an image size of 792 mm by 1,188 mm.
Step-by-step explanation:
To determine how far away the screen should be if a slide is placed 103 mm from a 100 mm focal length lens and produces a sharp image, we use the lens formula:
1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens.
Given that f = 100 mm and do = 103 mm, we can rearrange the formula to solve for di:
1/di = 1/f - 1/do. Plugging in the values: 1/di = 1/100 mm - 1/103 mm, which gives us di = 3,400 mm. So, the screen should be 3,400 mm away from the lens.
To find the dimensions of the image of a 24.0 mm by 36.0 mm slide, we can use the magnification formula: m = -di/do, where m is the magnification. The negative sign indicates that the image is inverted. Substituting the known values, we get m = -3,400 mm / 103 mm. Now, we can find the dimensions of the image by multiplying the size of the object by the magnification, which gives us an image size of 792 mm by 1,188 mm.