A concave mirror forms a real image that is twice the size of the object. If the object is 20 cm from the mirror, the radius of curvature of the mirror must be about:13 cm20 cm27 cm40 cm
Question
A concave mirror forms a real image that is twice the size of the object. If the object is 20 cm from the mirror, the radius of curvature of the mirror must be about:13 cm20 cm27 cm40 cm
Solution
The mirror formula is given by 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Given that the image is real and twice the size of the object, the magnification (m) is -2 (negative because the image is inverted).
The magnification is also given by the ratio of the image distance to the object distance (m = -v/u).
So, -2 = -v/(-20 cm)
Solving for v gives v = 40 cm.
Substituting v = 40 cm and u = -20 cm into the mirror formula gives 1/f = 1/40 cm + 1/-20 cm = -1/40 cm.
So, f = -40 cm.
The radius of curvature (R) of a mirror is twice its focal length (R = 2f).
So, R = 2*(-40 cm) = -80 cm.
However, the radius of curvature is usually considered as a magnitude, so we take the absolute value, giving R = 80 cm.
Therefore, none of the given options are correct. The radius of curvature of the mirror should be approximately 80 cm.
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