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A concave mirror has a focal length of 43 cm. what is the position of the resulting image if the image is inverted and 5 times smaller than the object?

A) 86 cm in front of the mirror
B) 43 cm in front of the mirror
C) 17.2 cm in front of the mirror
D) 8.6 cm in front of the mirror

1 Answer

3 votes

Final answer:

The image formed by the concave mirror with a focal length of 43 cm and an image that is inverted and five times smaller than the object is located at 17.2 cm in front of the mirror, making option C the correct answer.

Step-by-step explanation:

The question involves finding the position of the image formed by a concave mirror when given the focal length and the size of the image relative to the object.

To solve this, we need to use the mirror equation 1/f = 1/do + 1/di, where f is the focal length, do is the distance of the object from the mirror, and di is the distance of the image from the mirror.

Additionally, the magnification m is given by di/do and for an inverted image that is five times smaller than the object, m would be -1/5, because the negative sign indicates that the image is inverted.

Given that the focal length is 43 cm (which we will consider as positive since it's a concave mirror), we can rewrite the mirror equation in terms of the do and solve for the image distance di considering the magnification.

Substituting m into the equation we get: -1/5 = di/do, therefore do = -5di. Now, substituting do into the mirror equation, we can solve for di. After calculations we find that the image is formed at 17.2 cm in front of the mirror, making option C the correct option.

User Jon Rubins
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