Final answer:
The screen should be placed approximately 3.433 meters (3433.33 mm) from the lens for a sharp image. Using the magnification formula, the dimensions of the magnified image are found to be about 800.0 mm by 1200.0 mm.
Step-by-step explanation:
To determine how far away the screen should be for a sharp image when using a slide projector with a 100 mm focal length lens, the lens formula can be used: 1/f = 1/do + 1/di, where f is the focal length, do is the distance from the lens to the object (slide), and di is the distance from the lens to the image (screen).
For part (a), given do = 103 mm and f = 100 mm:
1/100 = 1/103 + 1/di
1/di = 1/100 - 1/103
1/di = (103 - 100) / (100 * 103)
1/di = 3 / 10300
di = 10300 / 3 = 3433.33 mm
Since the screen needs to be placed at the image distance, it should be approximately 3433.33 mm, or 3.433 m from the lens to get a sharp image.
For part (b), to find the dimensions of the image, we will use the magnification formula: m = -di/do. Since the slide dimensions are 24.0 mm by 36.0 mm, and the magnification (m) can be calculated from the image and object distances found previously:
m = -3433.33/103 ≈ -33.334
The negative sign indicates the image is inverted. The magnified image dimensions can then be calculated by multiplying the magnification by the original dimensions of the slide:
Height of image = m * height of slide = -33.334 * 24.0 mm ≈ -800.016 mm
Width of image = m * width of slide = -33.334 * 36.0 mm ≈ -1200.024 mm
So, the dimensions of the image are approximately 800.0 mm by 1200.0 mm.