Question

An aerial camera is suspended from a blimp and positioned at D. The camera needs to cover 125 meters of ground distance. If the camera hangs 10 meters below the blimp and the blimp

attachment is 20 meters in length, at what altitude from D to B should the camera be flown?

Answer 1

These questions pertain to the optical physics associated with cameras and lenses. They require understanding the principles of focal length, image formation, and magnification for objects at various distances, such as mountains and celestial bodies like the sun.

Step-by-step explanation:

Understanding Camera and Lens Physics

The questions presented involve calculations based on the optical physics of lenses and photography, specifically pertaining to focal length, object distance, and image height. Let's address each example provided:

1. With a 200 mm focal length telephoto lens photographing mountains 10.0 km away:

• (a) The image is typically formed at the focal point of the lens, so it would be 0.200 m (200 mm) from the lens. However, because the actual distance of the mountains far exceeds the focal length, the image location approaches the focal length on the film or sensor side of the lens.
• (b) The height of the image can be calculated using the lens formula and magnification, resulting in a significantly smaller image height compared to the actual size of the cliff. For a 1000 m high cliff, it would proportionally scale down based on the ratio of the focal length to the distance to the cliff.

When photographing the sun with a 100 mm focal length lens:

• The image of the sun will also be created very close to the focal point of the lens, as the sun's distance is much greater than the focal length.
• The height of the image on the film will be a function of the sun's actual diameter and its distance from Earth, scaled down by the lens's focal length. Using the small angle approximation, given the sun's diameter (1.40 × 106 km) and distance (1.50 × 108 km), the image height can be calculated.

When photographing a person 3.00 m away using a 50.0 mm lens:

• (a) The film must be placed slightly further than the lens's focal length from the lens to form a clear image, as determined by the lens equation (1/f = 1/v + 1/u), where f is the focal length, v is the image distance, and u is the object distance.
• (b) The fraction of the person's height that fits on the film can be determined by the magnification, which is the ratio of the image height to the object height (in this case, the height of the person).

Answer 2

The picture isn't quite clear, so i have include a clearer one in the attachment below.

We need to determine the altitude of segment BD. From taking a look at the picture I can conclude that these triangle( s ) formed through the camera's positioning are proportional to one another, but here is the evidence -

( By Vertical Angle's Theorem,
`m<FDE = m<ADC`

( By Alternate Interior Angle's Theorem,
`m< EFD = m<ACD`

( Respectively by Alternate Interior Angle's Theorem,
`m< FED = m<CAD`

Therefore we can conclude that these triangle are similar to one another, and hence we can create a proportionality as such ( with the lengths ) -

`20m / 125m = 10m / x`

And this " x " is the length of segment BD, which we want to determine -

`20 / 125 = 10 / x - ( Cross Multiply ),\\20x = 125( 10 ),\\20x = 1250,\\\\x = 1250 / 20,\\x = 62.5 m`

The altitude with which the camera should be flown is 62.5 meters.

Hope that helps!