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A building standing 100m from a pinhole camera produces on the screen of thecamera an image 5 cm high 10 cm behind the pinhole. Determine the actualheight of the building

Question

A building standing 100m from a pinhole camera produces on the screen of thecamera an image 5 cm high 10 cm behind the pinhole. Determine the actualheight of the building

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Solution

To determine the actual height of the building, we can use similar triangles and the concept of magnification in a pinhole camera.

Step 1: Identify the given information:

  • Distance from the building to the pinhole camera (object distance): 100m
  • Height of the image on the screen: 5cm
  • Distance from the image to the pinhole camera (image distance): 10cm

Step 2: Set up the proportion: We can set up a proportion using the similar triangles formed by the building, the pinhole camera, and the image on the screen.

Actual height of the building / Height of the image on the screen = Distance from the building to the pinhole camera / Distance from the image to the pinhole camera

Let's assign variables to the unknowns: Let x be the actual height of the building.

x / 5cm = 100m / 10cm

Step 3: Solve for x: Cross-multiply the proportion:

x * 10cm = 5cm * 100m

10x = 500cm * m

Step 4: Convert units: Since we want the answer in meters, we need to convert centimeters to meters. There are 100 centimeters in 1 meter.

10x = 5m * 100m

10x = 500m^2

Step 5: Solve for x: Divide both sides of the equation by 10:

x = 500m^2 / 10

x = 50m

Therefore, the actual height of the building is 50 meters.

This problem has been solved

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