Discover the Depth of an Opaque Cylindrical Tank with this Optics Question

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In summary, an opaque cylindrical tank with an open top has a diameter of 3m and is completely filled with water. When the afternoon sun reaches an angle of 28o above the horizon, the bottom of the tank is not illuminated. The depth of the tank can be calculated using the sine or cosine rule, with a result of approximately 1.41 m. The bottom of the tank is not illuminated because the sun is at a low angle in the afternoon.
  • #1
semc
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An opaque cylindrical tank with an open top has a diameter of 3m and is completely filled with water. When the afternoon sun reaches an angle of 28o above the horizon, sunlight cease to illuminate and part of the bottom of the tank. How deep is the tank?

I don't understand how to approach this question but more importantly I guess I should ask why doesn't the bottom part of the tank is not illuminated?
 
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  • #2
Hi,
To make things easier i suggest you to draw a schematic..
I think it is simple.Draw a cylinder..that is enough..Now draw a line..with 28 degree to the surface of the tank or to the bottom of the tank..now you can apply sin or cosine rule to get the height of cylinder? By this way i got 1.41 m height of cylinder.
good luck
 
  • #3
semc said:
… why doesn't the bottom part of the tank is not illuminated?

Hi semc! :smile:

It's afternoon, so the sun is going down …

even if the tank was empty, when the sun is low enough, the sunlight won't light up all the bottom of the tank. :wink:
 

1. What is the purpose of discovering the depth of an opaque cylindrical tank using optics?

The purpose of this question is to understand the practical application of optics in measuring the depth of a cylindrical tank. This information can be useful in industries such as oil and gas, agriculture, and manufacturing.

2. How does optics help in determining the depth of an opaque cylindrical tank?

Optics, specifically the principles of refraction and reflection, can be used to calculate the depth of a cylindrical tank. By measuring the angle of incidence and the refractive index of the liquid, the depth can be determined using simple trigonometric equations.

3. What are the factors that can affect the accuracy of determining the depth of an opaque cylindrical tank using optics?

The accuracy of this method depends on several factors such as the quality of the optics used, the uniformity of the liquid's refractive index, and the precision of the measurement of the angle of incidence. Other external factors like the shape of the tank and the presence of impurities in the liquid can also affect the accuracy.

4. Are there any limitations to using optics for measuring the depth of an opaque cylindrical tank?

Yes, there are limitations to this method. Optics can only be used to measure the depth of a cylindrical tank with a flat and transparent bottom. It cannot be used for tanks with irregular shapes or opaque bottoms. Additionally, the liquid inside the tank must have a known and consistent refractive index for accurate results.

5. Can other methods be used to determine the depth of an opaque cylindrical tank?

Yes, there are other methods that can be used to measure the depth of a cylindrical tank, such as ultrasonic sensors, pressure sensors, and float gauges. These methods may be more suitable depending on the specific tank and its contents.

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