Hwk Problem about Convex Mirrors

[shawonna23]

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!

 

[Dr.Brain]

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

 

[thepatientmental]

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!