The lens of a slide projector has a focal length of 10.0 cm. It is used to project the image of a 35 mm slide (24 mm × 36 mm) onto a square screen located 6.0 m away. Of the following screen widths, which is the smallest that would allow the entire image to fit?
A) 5.1 m
B) 4.4 m
C) 2.2 m
D) 1.1 m
E) 0.88 m

Question

Quizplus · Accepted Answer

To determine the size of the image projected onto the screen, we need to use the following formula:
(distance from lens to screen) / (focal length of lens) = (size of image) / (size of object)
Plugging in the values we know:
(6.0 m) / (10.0 cm) = (size of image) / (24 mm)
Solving for the size of the image, we get:
size of image = (6.0 m) / (10.0 cm) * (24 mm) = 14.4 m
Since the screen must be square and the image is rectangular, we need to take the minimum of the two dimensions of the image to ensure that it will fit entirely on the screen:
minimum dimension of image = min(24 mm, 36 mm) = 24 mm
To convert this to meters, we divide by 1000:
minimum dimension of image = 24 mm / 1000 = 0.024 m
Finally, to determine the size of the screen we need, we use the formula:
size of screen = (size of image) / (distance from lens to screen)
Plugging in the values we know:
size of screen = 14.4 m / 6.0 m = 2.4 m
Since we need the screen to be square, the smallest possible width that will allow the entire image to fit is:
minimum screen width = min(2.4 m, 2.4 m) = 2.4 m
Therefore, the correct answer is C) 2.2 m, which is the only option smaller than 2.4 m.

The Lens of a Slide Projector Has a Focal Length