Finding distance of image from mirror given focal length

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To find the distance of the image from a concave mirror with a focal length of 40 cm when the object is very far away, the mirror formula 1/u + 1/v = 1/f is applied. Given that the object distance (u) approaches infinity, the image distance (v) simplifies to the focal length, resulting in an image distance of 40 cm. The image formed is real since it is located outside the focus when the object is at a large distance. As the object distance increases, the image distance remains constant at 40 cm. Therefore, the solution confirms that the image is real and positioned 40 cm from the mirror.
RabbitWho
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Homework Statement


An object is at a very large distance from a concave mirror of focal length 40cm. Find the distance from the image to the mirror. Is the image real or virtual?

Homework Equations


1/u + 1/v = 1/f

The Attempt at a Solution


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1/u + 1/v = 1/40

The image has to be real because it must be outside the focus if it is very far from the mirror, right?
It seems to me like I haven't got enough information to solve the problem. How would I go about doing it? The answer from the key is 40cm.
 
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What do you get if you put in a very large number (say, 10000cm) for the object distance? What happens as that distance gets even farther?
 
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