What is the image distance for a concave mirror using the mirror equation?

In summary, to find the image distance using the mirror equation, you need to use the formula 1/do + 1/di = 1/f, where do represents the object distance, di represents the image distance, and f represents the focal length. Given a do of 2cm and f of 4cm, the image distance is calculated to be -4cm, which is a negative value because it is a virtual image behind the mirror.
  • #1
toothpaste666
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Homework Statement


mirrorq.png

B) Using the mirror equation, find the image distance.

Homework Equations


1/do + 1/di = 1/f

The Attempt at a Solution


mirrorrays.png
[/B]
B)
do = 2cm f = 4cm
1/do + 1/di = 1/f
1/di = 1/f - 1/do
1/di = do/f(do) - f/f(do)
1/di = (do-f)/(f*do)
di = (f*do)/(do-f) = (4cm * 2cm)/(2cm - 4cm) = (8cm^2)/(-2cm) = -4cm
di = -4cm

 
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  • #2
is it ok that my image distance came out negative? if i am correct this is fine if the image is behind the mirror
 
  • #3
It is correct, the distance of a virtual image is negative in the frame of sign convention you applied.
 
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  • #4
thank you!
 
  • #5


I would like to point out that the image distance, di, is a negative value in this case. This indicates that the image formed by the concave mirror is a virtual image, meaning it cannot be projected onto a screen. This is because the object distance, do, is less than the focal length, f, of the mirror. In other words, the light rays do not actually converge at a point to form a real image. This result is in line with the properties of concave mirrors, which are known to produce virtual images when the object is placed within the focal length of the mirror. It is important to consider the sign conventions and understand the physical interpretation of the results when solving problems involving mirrors and lenses.
 

Related to What is the image distance for a concave mirror using the mirror equation?

1. What is a concave mirror?

A concave mirror is a type of curved mirror where the reflective surface curves inward, like the inside of a spoon. This shape causes light rays that strike the mirror to converge at a specific point, known as the focal point.

2. How does ray tracing work for concave mirrors?

Ray tracing is a method used to determine how light rays will behave when they interact with a concave mirror. The process involves tracing the path of a few key light rays from an object to the mirror, and then reflecting them off the mirror according to the laws of reflection. By tracing multiple rays, we can determine the location and characteristics of the resulting image.

3. What is the difference between real and virtual images in concave mirrors?

In a concave mirror, a real image is formed when the light rays actually converge at a point in front of the mirror, and can be projected onto a screen. A virtual image is formed when the light rays only appear to be coming from a point behind the mirror, and cannot be projected onto a screen. Real images are always inverted, while virtual images can be either upright or inverted.

4. What factors affect the image produced by a concave mirror?

The image produced by a concave mirror is affected by the object distance (distance between the object and the mirror), the focal length of the mirror, and the size of the mirror. The position and size of the resulting image can be calculated using the thin lens equation and magnification equation.

5. How is concave mirror used in everyday life?

Concave mirrors have many practical applications in everyday life. They are used in car headlights, flashlights, and spotlights to focus light and create a bright beam. They are also used in telescopes and binoculars to magnify distant objects. Concave mirrors are also commonly used in makeup and shaving mirrors, as well as in solar cookers to concentrate sunlight and create heat.

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