Calculating Rearview Mirror + Amusement Park Mirror Images

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In summary, the first question involves using the equation (1/object distance) + (1/image distance) = 1/f, taking into account that the sideview mirror on a car is a diverging mirror with a negative focal length. The second question may require the use of the magnification equation, which states (h_image / h_object) = (d-image / d_object). It is also noted that only a diverging mirror can create an upright and larger image.
  • #1
chase222
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I have 2 questions:
What type and height of image would a rearview mirror produce of a car that was 1.3 m high and 15.0 m behind you, assuming the mirror's radius of curvature is 3.2 m?

I don't know what equation to use to solve the problem. I think it might be:
(1/object distance) + (1/image distance) = 1/f

However, w/ this equation I don't know where to plug in the height (1.3 m). Please help!

The other question is:
A mirror at an amusement park shows an upright image of any person who stands 1.3 m in front of it. If the image is three times the person's height, what is the radius of curvature?

However, I don't understand how to solve it if we don't know how big the image is. I also know that f=r/2, which I might need later on in the problem.

Thanks!
 
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  • #2
You noticed that f = r/2. You need this for the first question along with the knowledge that the sideview mirror on a car is a diverging mirror. THis means that the focal length must have a negative sign. You have the correct equation, just remember to use a negative focal length.

There is also the magnification equation which says (h_image / h_object) = (d-image / d_object). You might find this useful for both questions.

And only a diverging mirror (positive focal length) can create an upright AND larger image.
 
  • #3


For the first question, you are correct in using the equation (1/object distance) + (1/image distance) = 1/f. The height of the object (car) is not needed in this equation. Instead, you will need to know the distance of the object from the mirror (15.0 m) and the radius of curvature (3.2 m). You can then solve for the image distance, which will give you the height of the image produced by the rearview mirror.

For the second question, you are correct in using the equation f=r/2. You will also need to use the equation (1/object distance) + (1/image distance) = 1/f. The height of the image is given as three times the person's height, so you can plug in 3.9 m (1.3 m x 3) for the image distance. You can then solve for the object distance, which will give you the distance of the person from the mirror. Once you have both the object distance and the image distance, you can use the equation f=r/2 to solve for the radius of curvature. Hope this helps!
 

FAQ: Calculating Rearview Mirror + Amusement Park Mirror Images

1. How do you calculate rearview mirror images?

To calculate a rearview mirror image, you need to use the law of reflection, which states that the angle of incidence is equal to the angle of reflection. This means that the reflected image will appear the same distance behind the mirror as the object is in front of the mirror. You can use this information to determine the size and location of the reflected image.

2. What is the difference between a rearview mirror and an amusement park mirror?

The main difference between a rearview mirror and an amusement park mirror is the type of reflection they produce. Rearview mirrors are designed to produce a clear, accurate reflection of objects behind the vehicle, while amusement park mirrors are intentionally distorted to create funhouse effects.

3. How do you calculate amusement park mirror images?

Calculating amusement park mirror images is similar to calculating rearview mirror images, but with the added factor of distortion. The law of reflection still applies, so the angle of incidence will be equal to the angle of reflection. However, the reflected image will be distorted due to the curved or angled surface of the mirror. This can make determining the size and location of the reflected image more challenging.

4. What factors affect the reflection in a rearview mirror?

The main factors that affect the reflection in a rearview mirror include the angle of incidence, the curvature of the mirror, and the position of the viewer. The angle of incidence determines the angle of reflection, while the curvature of the mirror can affect the size and clarity of the reflected image. The position of the viewer can also impact the reflection, as it may change the angle at which the light hits the mirror.

5. How does the shape of a mirror affect the reflection?

The shape of a mirror can greatly affect the reflection it produces. Flat mirrors produce a clear, undistorted reflection, while curved mirrors can create magnified or distorted images. The positioning of the mirror can also impact the reflection, as a concave mirror will produce a different reflection than a convex mirror. Additionally, the surface of the mirror can also affect the reflection, as a smooth surface will produce a clearer reflection than a rough surface.

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