A concave mirror forms a real image which 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:

Question

Quizplus · Accepted Answer

Given that the image is real and twice the size of the object, the magnification (m) is -2 (negative sign because the image is real and inverted). The magnification formula for mirrors is m = -v/u, where v is the image distance and u is the object distance. Given m = -2 and u = -20 cm (object distance is negative for mirrors), we can solve for v: -2 = -v/-20, which gives v = -40 cm (negative because the image is on the same side as the object for concave mirrors).The mirror equation is 1/f = 1/v + 1/u, where f is the focal length. Substituting v = -40 cm and u = -20 cm, we get 1/f = 1/(-40) + 1/(-20) = -1/40 - 1/20 = -3/40. Therefore, f = -40/3 cm. The radius of curvature (R) is 2f, so R = 2*(-40/3) = -80/3 cm, which is approximately -26.67 cm. The negative sign indicates that the radius of curvature is on the same side as the object for concave mirrors, but the magnitude is what we're interested in, which is approximately 27 cm.

A Concave Mirror Forms a Real Image Which Is Twice