Question

The owners of the Movie Palace use the Illuminator 100 light bulb in their projectors, but are now considering switching to the Illuminator 100 Plus, a more powerful light bulb that projects movies onto larger screens farther away. The Illuminator 100 Plus projects movies onto screens 108 feet wide and 180 feet from the projector, while the Illuminator 100 projects movies onto screens only 81 feet wide, as shown in the figure below. How much farther from the projector, in feet, is the screen for the Illuminator 100 Plus than the screen for the Illuminator 100 ?

Answer 1

To find the difference in distance between the screens of the Illuminator 100 and Illuminator 100 Plus projectors, we need to calculate the distance of each screen. This can be done using the formula for the focal length of the lens. Once we have the distances, we can subtract them to find the difference.

Step-by-step explanation:

To find the difference in distance, we need to subtract the distance of the Illuminator 100 screen from the distance of the Illuminator 100 Plus screen. The Illuminator 100 screen is 81 feet wide and we need to calculate the distance, given the focal length of the lens and the distance of the slide from the lens. The formula is:

1/f = 1/do + 1/di

Where f is the focal length, do is the distance of the slide from the lens, and di is the distance of the image from the lens.

We can use this formula to calculate the distance of the screen for the Illuminator 100. Then, we can use the same formula to calculate the distance of the screen for the Illuminator 100 Plus. Finally, we subtract the two distances to find the difference in distance between the two screens.

Answer 2

Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;

Illuminator 100 plus bulb

It movies onto screens ;

108 ft wide

180 ft away from the projector

Illuminator 100 bulb

81 ft wide

? : from the projector

Here apply the idea of similarity ratios where;

The ratio