tbr test mirror question

[2010premed]

The image of an object that is far from a concave mirror has what location relative to the mirror and its focal point?
Answer: image forms at the focal point
This is b/c 1/f = 1/I + 1/o
1/0 = 1/ infinity therefore 1/0 = 0
1/f=1/I so image forms at the focal point.
However, the explanation says that this is only true for concave mirrors and lenses? What if they were convex??

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[PiBond]

The image of an object that is far from a concave mirror has what location relative to the mirror and its focal point?
Answer: image forms at the focal point
This is b/c 1/f = 1/I + 1/o
1/0 = 1/ infinity therefore 1/0 = 0
1/f=1/I so image forms at the focal point.
However, the explanation says that this is only true for concave mirrors and lenses? What if they were convex??

gotta flip the sign on the focal point, since it's behind the mirror it's negative

 

[2010premed]

right, so that would make it 1/-f = 1/i, so the image is at the negative focal point? so if f = 2, then i = -2, which means for a convex lens, then image would be on same side of the object, and if it's a convex mirror, then the image is on the opposite side of the object?

 

[BerkReviewTeach]

right, so that would make it 1/-f = 1/i, so the image is at the negative focal point? so if f = 2, then i = -2, which means for a convex lens, then image would be on same side of the object, and if it's a convex mirror, then the image is on the opposite side of the object?

Exactly! If o is at infinity, then according to the equation, 1/o = 0 so we get 1/f = 1/i, where f is a negative number so i must also be a negative number (making it a virtual image at the virtual focal point).

In general with diverging lenses and mirrors, because f is a -#, we get always get a negative number for i that is less in magntiude than both o and f:

1/(-#) = 1/(+#) + 1/(i)

i must be a -# that is smaller in magnitude than o and with a limit of f (as you just showed in your extreme example), so that the math works out. This means that the image is ALWAYS virtual, closer to the lens or mirror than the object is, and found between the lens or mirror and the virtual focal point.

In the BR lectures and the soon to be released ( ) physics book, they make a big point that diverging lenses and mirrors ALWAYS give you an SUV (Smaller, Upright, Virtual image).