A concave mirror has a focal length of 49.0 cm. (a) What is its radius of curvat

Question

A concave mirror has a focal length of 49.0 cm.
(a) What is its radius of curvature?
=_______ cm

(b) Locate the image when the object distance is 100 cm. (Indicate the side of the mirror with the sign of your answer.)
=_______cm

Describe the properties of the image when the object distance is 100 cm. (Select all that apply.)
yes or no.....
real=
virtual=
upright=
inverted=

(c) Locate the image when the object distance is 10.0 cm. (Indicate the side of the mirror with the sign of your answer.)
=_______ cm

Describe the properties of the image when the object distance is 10.0 cm. (Select all that apply.)
yes or no.....
real=
virtual=
upright=
inverted=

Explanation / Answer

Part A)

The radius of curvature of a mirror is twice the focal length

R = 2f = 2(49) = 98 cm

Part B)

The equation here is

1/f = 1/p + 1/q

1/49 = 1/100 + 1/q

q = 96 cm   (positive value means image in front of mirror)

Since q is positive, the image is real. The image will also be inverted and that can be seen by the magnification formula where M = -q/p. The value of the magnification would come out negative indicating the inversion

Part C)

1/f = 1/p +1/q

1/49 = 1/10 + 1/q

q = -12.6 cm (Negative value means image in back of the mirror)

The negative also indicated that the image is virtual. The magnification will come out positive, so the image is upright.

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