During a daytime football game you notice that a player's reflective helmet forms an image of the sun 4.3 cm behind the surface of the helmet. what is the radius of curvature of the helmet, assuming it to be roughly spherical.

Why is the helmet considered as concave, isn't it convex?

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The player's reflective helmet forms an image of the sun 4.3 cm behind the surface of the mirror. The helmet is approximated to a spherical mirror. Let the radius of the mirror be r. The image distance i, object distance o and the focal length f are related by:

1/o + 1/i = 1/f

The object distance which is the distance of the sun from the mirror can be taken as infinity, this gives:

1/f = 1/4.3

=> f = 4.3

The radius of the mirror is equal to twice the focal length or 8.6 cm. The helmet is not considered as a concave mirror, it is a convex mirror which is the reason why the image of the sun is formed behind the surface of the mirror in all cases.

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