Final answer:
To design a concave mirror that will produce a virtual image two times bigger when the object is placed 20 cm from the mirror, we can use the mirror formula and the magnification formula to find the image distance and focal length. The radius of curvature is equal to twice the focal length.
Step-by-step explanation:
To design a concave mirror that will produce a virtual image two times bigger when the object is placed 20 cm from the mirror, we can use the mirror formula. The mirror formula states that 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
In this case, we are given that the magnification (m) is 2 and the object distance (do) is 20 cm. We can use the magnification formula, m = -di/do, to find the image distance (di).
Since the magnification is positive, the image is virtual. Plugging in the values, we get m = -di/20 cm, which gives us di = -40 cm. Since the image distance is negative, the image is virtual and located on the same side as the object. Thus, the radius of curvature (R) of the mirror is equal to twice the focal length (f).
R = 2f
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