How Do You Calculate the Focal Length of a Concave Mirror with a Moving Image?

In summary, to calculate the focal length of a concave mirror with a moving image, you can use the formula 1/f = 1/u + 1/v, where f is the focal length, u is the object distance, and v is the image distance. By adjusting the position of a known object, measuring the corresponding image distance, and plugging the values into the formula, you can accurately determine the focal length of the concave mirror. It is important to note that this method only works for concave mirrors, as convex mirrors have a negative focal length and require a different formula for calculation.
  • #1
premed_love
19
0

Homework Statement


A light bulb is placed 10.7 cm in front of a concave mirror. When the concave mirror is replaced by a plane mirror in the same location, the bulb's image moves 4.00 cm closer to the mirror. Calculate the focal length of the concave mirror.

I am given: do: 10.7
and 4.00 is Di

Homework Equations


Mirror equation: 1/di+1/do=1/f

The Attempt at a Solution



I know I have to use the mirror equation so I did. However, I also added 10.7 and 4.00 to get a new di.

1/10.7+1/14.7=1/f
Eventually, I get 6.19 which is wrong! Anyone would like to help me see what is wrong?[/B]
 
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  • #2
premed_love said:

Homework Statement


A light bulb is placed 10.7 cm in front of a concave mirror. When the concave mirror is replaced by a plane mirror in the same location, the bulb's image moves 4.00 cm closer to the mirror. Calculate the focal length of the concave mirror.

I am given: do: 10.7
and 4.00 is Di

Homework Equations


Mirror equation: 1/di+1/do=1/f

The Attempt at a Solution



I know I have to use the mirror equation so I did. However, I also added 10.7 and 4.00 to get a new di.

1/10.7+1/14.7=1/f
Eventually, I get 6.19 which is wrong! Anyone would like to help me see what is wrong?[/B]
Which side of the mirror is the new image? (It's not made clear.)
What's the sign convention for object and image distances when dealing with mirrors?
(What would your equation produce for the flat mirror?)
 
  • #3
haruspex said:
Which side of the mirror is the new image? (It's not made clear.)
What's the sign convention for object and image distances when dealing with mirrors?
(What would your equation produce for the flat mirror?)
The only information I am given is the one I have provided. I am told it is a concave mirror- that's it.
 
  • #4
premed_love said:
The only information I am given is the one I have provided. I am told it is a concave mirror- that's it.
In order to write the equation you used, you have to make an assumption about whether the object and image are on the same side of the mirror or on opposite sides. Which did you assume? Is your equation correct for that assumption?
 
  • #5
haruspex said:
In order to write the equation you used, you have to make an assumption about whether the object and image are on the same side of the mirror or on opposite sides. Which did you assume? Is your equation correct for that assumption?

I was thinking the image should be real and on the same side which is why my Di would not be negative.1/10.7+1/14.7=1/f which is why I get
eventually, I get 6.19. Are you trying to imply that my di is negative and my equation should be 1/10.7-1/14.7=1/f
 
  • #6
premed_love said:
I was thinking the image should be real and on the same side which is why my Di would not be negative.1/10.7+1/14.7=1/f which is why I get
eventually, I get 6.19. Are you trying to imply that my di is negative and my equation should be 1/10.7-1/14.7=1/f
I'm saying it's a strong possibility. Note that the question says
premed_love said:
When the concave mirror is replaced by a plane mirror in the same location, the bulb's image moves 4.00 cm closer to the mirror
It doesn't say "is 4cm closer" or "moves to 4cm closer and on the opposite side". That suggests to me it moves by 4cm, not by 10.7+14.7=25.4 cm.
 
  • #7
So you would think it be a simple mirror equation then: 1/10.7+1/4.0=1/f so 2.94
 
  • #8
but 2.94 cm is off. I am so confused!
 
  • #9
premed_love said:
So you would think it be a simple mirror equation then: 1/10.7+1/4.0=1/f so 2.94
No, we're discussing what sign is appropriate to use in your original equation. The distances are correct, but are the image and object the same sign or opposite signs?
 
  • #10
haruspex said:
No, we're discussing what sign is appropriate to use in your original equation. The distances are correct, but are the image and object the same sign or opposite signs?
I think they will be the same size
 
  • #11
I think they will be the same sign.
 
  • #12
premed_love said:
I think they will be the same sign.
Why?
 
  • #13
haruspex said:
Why?
Because it's a concave mirror. The image is also real. Earlier I was thinking they would be different signs as 4.00 cm is moving closer. But then the concave part made me think the sign would be the same.
 
  • #14
premed_love said:
Because it's a concave mirror. The image is also real. Earlier I was thinking they would be different signs as 4.00 cm is moving closer. But then the concave part made me think the sign would be the same.
Read http://en.wikipedia.org/wiki/Curved_mirror#Image_2
 

1. What is a concave mirror problem?

A concave mirror problem refers to a type of optical problem in which a concave mirror is used to reflect light. This type of problem is common in physics and optics, and it involves determining the position, size, and orientation of an image formed by a concave mirror.

2. How do you solve a concave mirror problem?

To solve a concave mirror problem, you need to use the laws of reflection and the properties of concave mirrors. You also need to understand the relationship between object distance, image distance, and focal length. By applying these principles and using appropriate equations, you can determine the characteristics of the image formed by a concave mirror.

3. What is the difference between a concave and convex mirror?

A concave mirror curves inward and has a reflective surface on the inside, while a convex mirror curves outward and has a reflective surface on the outside. In a concave mirror, light rays that are parallel to the mirror's axis converge at a point after reflection, while in a convex mirror, the rays diverge after reflection. This results in different image characteristics for each type of mirror.

4. What are the uses of concave mirrors?

Concave mirrors have various practical uses, such as in telescopes, solar furnaces, and headlights of cars. They are also used in many scientific experiments and demonstrations, such as the famous "burning paper with a concave mirror" experiment. Concave mirrors are also used in makeup mirrors and shaving mirrors, as they can produce magnified images of the face.

5. What are some common misconceptions about concave mirrors?

One common misconception about concave mirrors is that they always produce magnified images. In reality, the size of the image depends on the object distance and the focal length of the mirror. Another misconception is that concave mirrors can only produce virtual images. In certain cases, concave mirrors can also produce real images, such as when the object is placed beyond the focal point. Additionally, many people believe that concave mirrors are only used for magnifying objects, but they have various other uses, as mentioned in the previous answer.

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