An object 5.00 cm tall is placed at the zero mark of a meter stick. (A meter sti

Question

An object 5.00 cm tall is placed at the zero mark of a meter stick. (A meter stick is one meter long). A spherical mirror located at some point on the meter stick creates an upright image of the object. The image created is 2.00 cm tall, and the image is located at the 42.0-cm mark on the meter stick. (a) Is mirror or concave? Justify your answer! A correct "guess" will receive zero points. (b) Where on the meter stick is the mirror located? (c) What is the mirror's focal length (include the correct sign)?

Explanation / Answer

(A) Image is upright hence it is virtual image.

For virtual image case:

Convex mirror -> always make smaller image

Concave mirror -> virtual formed is always enlarged.

5 cm object to 2cm tall image.

image is diminshed hence this is convex mirror.

(B) suppose mirror is at mark x.

object distance, p = x

image distance, q = x - 42

m = - q / p = hi / ho

42 - x / x = 2 / 5

210 -5x = 2x

x = 30 cm

(c) p = 30 cm

q = 30 - 42 = - 12 cm

1/f = 1/p + 1/q

1/f = 1/30 + 1 /(-12)

f = -20 cm

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