2. Consider a concave mirror with curvature R. An ant of height h walks towards

Question

2. Consider a concave mirror with curvature R. An ant of height h walks towards the mirror along the optical axis at speed v. (a) When the ant's location is 2R from the mirror, where is the image of the ant? (b) Is the image real or virtual? (c) How big is the image of the ant? Upright or upside down? (d) Check your answers to (a), (b), and (c) with a quick ray tracing sketch. (e) The ant is actually moving so the image of the ant must be moving, too. Check with ray tracing what must be happening to the image of the ant. (f) Calculate how fast the image of the ant seems to be moving and interpret the sign to check if it matches your ray tracing in part (e).

Explanation / Answer

Mirror equation,

1/f = 1/do + 1/di

For concave mirror, f is positive , we know that R = 2f

so, f = R/2

1/di = 1/f - 1/do

1/di = 2/R - 1/ 2R

1/di = 3/2R

so, di = 2R/3

as image distance is positive, image is real and inverted.

also

hi / ho = -di / do

hi / h = - 1/3

hi = - h / 3

image is inverted

As the object moves towards the mirror the image location moves further away from the mirror and the image size grows (but the image is still inverted). When the object is that the focal point, the image is at infinity. As the object moves towards the mirror inside the focal point the image becomes virtual and upright behind the mirror.

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