PhysicsBowl 2018 Q29

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PhysicsBowl 2018

29) This question asks us to find the focal length of the convex mirror, given some information about an object and the image produced. The question specifies that this is a convex mirror; convex mirrors produce diverging lenses, which tells us that the focal length is negative.

This is the formula used to find the focal length for lenses and mirrors.

Where f is the focal length, d[o] is distance from the object to the mirror, and d[i] is the distance from the image to the mirror

We are given the distance of the image, but we still need to solve for the distance of the object in order to solve for the focal length. Let's use the magnification of the image to do this.

Where M is magnification, h[i] is the height of the image, h[o] is the height of the object, d[i] is the distance between the image and the mirror, and d[o] is the distance between the object and the mirror

Next, we can use d[o] and the given d[i] to solve for the focal length using the orange equation we started with.

Where f is the focal length, d[o] is distance from the object to the mirror, and d[i] is the distance from the image to the mirror

Answer: A