A concave mirror is used to form an image of an object. The object distance (u) is 30 cm
and the image distance (v) is 15 cm. Calculate the focal length (f) of the mirror.
-
A.
−10 cm
-
B.
−30 cm
-
C.
10 cm
-
D.
30 cm
Correct Answer:
A. −10 cm
Explanation:
To find the focal length of a concave mirror, use the mirror formula: 1/f = 1/v + 1/u. According to the Cartesian sign convention for a real image formed by a concave mirror, the object distance (u) and image distance (v) are both negative because they are measured in front of the mirror.
Given:
u = -30 cm
v = -15 cm
Plugging these into the formula:
1/f = 1/(-15) + 1/(-30)
1/f = -2/30 - 1/30
1/f = -3/30
1/f = -1/10
Therefore, f = -10 cm. The negative sign indicates that the focal point is located in front of the concave mirror.
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