Start a Fire with Shaving Mirror?

In summary, the conversation discusses using a concave shaving mirror to start a fire using sunlight. The focal length of the mirror is estimated to be 1m and the energy received per unit area from the sun is calculated. The conversation also mentions the Stefan-Boltzmann law and the heat energy required to raise the temperature of the paper. Finally, it is mentioned that the question does not provide any figures except for the temperature at which paper ignites. The conversation concludes that using a typical concave shaving mirror can focus all the energy on a small area, causing the paper to ignite.
  • #1
Master J
226
0
If paper ignites at 500 C, can one start a fire with a typical shaving mirror using sun light?


Since the only time a concave mirror has an upright, virtual, magnified image is with the object between the mirror and focus, I estimate a focal length of about 1m.

Now, the sun is at infinity, so all its light is passed thru the focus. This is where I get stuck. How do I relate the magnification of the mirror to the increase in intensity. I could then use Stefan- Boltzmann to get an idea of temperature, but I am stuck here. Any ideas?


Thanks!
 
Physics news on Phys.org
  • #2
If they're saying that a shaving mirror is to be used, its a plain mirror with infinite focal length.

What you have to do is calculate the energy received per unit area from the sun. Now, the let the energy recived per unit area be [tex]l[/tex] (I forget the symbol usually used for this constant).

Let the surface area of the mirror be [tex] A[/tex].

We'll assume that all of the energy falling on the mirror falls on the paper normally.

Let the ambient temperature be [tex]T_0[/tex] and the temperature of the paper at any time t be [tex]T[/tex].

As the paper is not a perfect black body, the law is of the form:

[tex]P=\sigma \epsilon AT^4[/tex]

where P represents the power absorbed by the paper.
As the paper will also radiate energy to its surroundings, our law takes the form

[tex]P=\sigma \epsilon A(T-T_0)^4[/tex]

Power is energy per unit time or [tex]P=\frac{dE}{dt}[/tex].

This is when I'm a little shaky on the subject. It's been a long time since I've done these problems so I may make a mistake.

If I remember correctly, the heat energy required to raise the temperature by a value [tex]\delta T[/tex] is given by:

[tex] q=mc\delta T[/tex]

Where m is the mass of the paper and C is a thermodynamic constant.

From the earlier equation we know,

[tex]P=\frac{dE}{dt}[/tex]

Simplifying the above experssion we have E=P.t

Equate this to q and you should be able to get a result.

Please double check my work as I may have made a mistake. There are many, more capable posters on this forum and I'm a little out of touch.
 
  • #3
Thanks for the input...I'll go thru your solution shortly.However, the question says "typical concave shaving mirror". I thought that was usually the case since one would normally like to magnify the image?

I should add that no figures are given for the question except the temperature at which paper ignites.
 
  • #4
Master J said:
Thanks for the input...I'll go thru your solution shortly.


However, the question says "typical concave shaving mirror". I thought that was usually the case since one would normally like to magnify the image?

I should add that no figures are given for the question except the temperature at which paper ignites.

In that case, all the energy is focused on a very small area. At the focal point of the mirror, the energy/unit area will be maximum and the paper will ignite after a time.
 
  • #5


I would say that it is possible to start a fire with a shaving mirror using sunlight, but it would require careful positioning and calculation. The key factor in starting a fire is the concentration of sunlight onto a small point, which increases the intensity of the light and creates enough heat to ignite the paper.

To calculate the focal length needed for the mirror, you would need to consider the size of the mirror and the distance between the mirror and the paper. The closer the mirror is to the paper, the shorter the focal length needed.

Once you have the focal length, you could use the magnification formula to determine the increase in intensity of the sunlight. Then, you could use the Stefan-Boltzmann law to calculate the temperature at the focal point. However, keep in mind that this calculation would only give an estimate, as there are other factors, such as air flow and moisture, that can affect the ignition of the paper.

Overall, starting a fire with a shaving mirror using sunlight is possible, but it would require precise calculations and careful positioning of the mirror. It is also important to take safety precautions and be aware of the potential risks involved.
 

1. How does using a shaving mirror start a fire?

Using a shaving mirror to start a fire works based on the principle of reflection. When the sun's rays hit the mirror's reflective surface, they are concentrated and directed to a focal point, creating a hot spot that can ignite dry tinder and start a fire.

2. What type of shaving mirror is best for starting a fire?

A small, compact mirror with a highly reflective surface is best for starting a fire. Ideally, the mirror should be made of glass and have a metal backing to maximize reflection.

3. Can any type of sunlight be used to start a fire with a shaving mirror?

No, only direct sunlight can be used to start a fire with a shaving mirror. Indirect or diffused sunlight will not create a concentrated enough beam to ignite a fire.

4. Are there any safety precautions to keep in mind when starting a fire with a shaving mirror?

Yes, it is important to be aware of your surroundings and avoid pointing the reflected beam at anything flammable, such as dry grass or foliage. It is also important to use caution when handling the mirror to avoid accidentally starting a fire or injuring yourself.

5. Can a shaving mirror be used to start a fire in any weather conditions?

While a shaving mirror can be used to start a fire in a variety of weather conditions, it is most effective on sunny days with minimal cloud coverage. Rain or heavy cloud coverage can block or diffuse the sun's rays, making it difficult to create a concentrated beam for starting a fire.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
1K
Replies
18
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Replies
2
Views
26K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
9K
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Back
Top