Final answer:
The distance of the screen is 50 mm.
Step-by-step explanation:
To determine the distance of the screen when a slide is placed 100 mm from the lens and produces a sharp image, we can use the lens formula:
1/f = 1/v - 1/u
Where f is the focal length, v is the distance of the screen, and u is the distance of the slide from the lens.
Substituting the given values, we have:
1/100 = 1/v - 1/100
Simplifying the equation, we get:
1/v = 1/100 + 1/100
1/v = 2/100
Then, by taking the reciprocal of both sides, we find that the distance of the screen is 50 mm.