Hwk Problem about Convex Mirrors

When using the mirror equation to calculate the location of an image in a convex mirror, it is important to correctly use the sign convention. Imagining the mirror at the origin and considering distances to the right as positive and distances to the left as negative can help with this calculation.
  • #1
shawonna23
146
0
An object that is 31 cm in front of a convex mirror has an image located 20 cm behind the mirror. How far behind the mirror is the image located when the object is 19 cm in front of the mirror?


For this problem, I know I have to use the mirror equation but I keep getting the wrong answer. The answer I got was -12.3 cm. What am I doing wrong? Please help!
 
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  • #2
Maybe you are not using the sign convention correctly.I advice you to imagine that the convex-mirror is placed at the origin and the distances tot he right are to be taken positive and on the left to be taken negative.Use the simple mirror-formula and try to calculate it again using correct sign-convention.

Bj
 
  • #3


Hi there,

It seems like you are on the right track with using the mirror equation. However, the negative sign in your answer indicates that you have made a mistake in your calculation.

Let's review the steps of the mirror equation to see where the error may have occurred:

1. Identify the given values: Object distance (do) = 31 cm, Image distance (di) = 20 cm
2. Substitute the values into the mirror equation: 1/do + 1/di = 1/f, where f is the focal length of the convex mirror.
3. Rearrange the equation to solve for the unknown value, in this case, the image distance (di).
4. Substitute the given value for do = 19 cm into the equation and solve for di.
5. The resulting value for di should be a positive number, indicating that the image is located behind the mirror.

Double check your calculations and make sure you are using the correct units (cm) throughout the equation. Also, remember that the focal length of a convex mirror is always positive, so any negative values in your calculation should be a red flag.

I hope this helps you identify where the error may have occurred. Keep practicing and you will get the hang of it!
 

1. What is a convex mirror?

A convex mirror is a curved mirror with its reflective surface bulging outwards. This type of mirror is also known as a diverging mirror because it causes light rays to spread out.

2. How does a convex mirror form an image?

A convex mirror forms an image by reflecting light rays that strike its surface. The reflected rays diverge (spread out) and do not actually meet. The image formed by a convex mirror is virtual, meaning it cannot be projected onto a screen.

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

A convex mirror bulges outwards, while a concave mirror curves inwards. This results in different properties for each type of mirror. Convex mirrors always form virtual images, whereas concave mirrors can form both real and virtual images depending on the placement of the object.

4. How is the image formed by a convex mirror different from that of a plane mirror?

A plane mirror reflects light rays at the same angle that they strike the surface, resulting in a virtual image that is the same size and distance from the mirror as the object. However, a convex mirror reflects light rays at a wider angle, causing the image to appear smaller and further away from the mirror compared to the object.

5. What are some applications of convex mirrors?

Convex mirrors have a wide range of applications, including as side mirrors on vehicles, in safety and security mirrors to provide a wider field of view, and in decorative mirrors. They are also used in telescopes and other optical instruments to produce a wider field of view.

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