Image Location for a Double Concave Mirror (-20 in Focal Length)

In summary, a double concave lens with a focal length of -20 inches is used and the image seems to be located at a distance of -18.9 inches when the object is 30 feet away from the lens. The negative sign indicates that the image is virtual and on the same side of the lens as the object. The lens equation and sign convention were used to determine this.
  • #1
cowgiljl
63
1
if a double concave mirror with a focal length f = -20 inches is used , where does the image seem to be located , if the image is 30 feet away from the lens

first i converted the 30ft to inches and got 360inches
used formula 1/p + 1/q = 1/f
.0028 + 1/q = -.05
1/q = -.053
q = -18.9 inches

is this correct
 
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  • #2
lens, not mirror

I assume you mean a double concave lens, not mirror. (A diverging lens.) And I also assume you are asked to find the image distance when the object is 30 feet away. If so, you are correct. But what does the negative sign mean? (The negative sign is correct; I'm just checking that you know where the image is.)
 
  • #3
not sure really where the image is i didn't think you could have a negitive distance

joe
 
  • #4
the sign in front tells you where the image is situated.
either in front if it's virtual or at the back if it's real.
so in your case I would say that the image is virtual because the sign is negative.
I think anyway haha :)
 
  • #5
cowgiljl said:
not sure really where the image is i didn't think you could have a negative distance
Just as I suspected! :eek:

To use the lens equation, you need to know the sign convention:

For converging lenses f is +, for diverging f is -
Object distance is always + (except for virtual objects)
Image distance is + for real images, - for virtual images

If the object is on the left of the lens, a real image (positive image distance) is on the right of the lens, while a virtual image (negative image distance) would be on the left.

In this case the image is virtual: it's on the same side of the lens that the object is on.
 
  • #6
thanks for that information because I was going to ask the question tuesday
 

1. How does the focal length affect the image location of a double concave mirror?

The focal length of a double concave mirror is a measure of how strongly the mirror converges or diverges light. A shorter focal length (-20 in this case) means that the mirror will converge the light more strongly, resulting in a closer image location compared to a mirror with a longer focal length.

2. How is the image location calculated for a double concave mirror?

The image location for a double concave mirror can be calculated using the formula:
1/f = 1/do + 1/di
Where f is the focal length, do is the object distance, and di is the image distance.

3. Can the image location be negative for a double concave mirror?

Yes, the image location can be negative for a double concave mirror. This indicates that the image is located behind the mirror and is a virtual image, meaning it cannot be projected onto a screen. A negative image location is characteristic of a diverging mirror.

4. How does the object distance affect the image location for a double concave mirror?

The object distance is the distance between the object and the mirror. As the object distance increases, the image distance decreases, resulting in a closer image location. This relationship is described by the formula in question 2.

5. Can the image location be the same as the object distance for a double concave mirror?

Yes, it is possible for the image location to be the same as the object distance for a double concave mirror. This occurs when the object is placed at the focal point of the mirror, resulting in an image distance of infinity. In this case, the image is formed at the same location as the object, resulting in a magnification of 1.

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