A real image formed by a concave mirror is 9.0 cm away from the object, measured
ID: 1701575 • Letter: A
Question
A real image formed by a concave mirror is 9.0 cm away from the object, measured along the central axis of the mirror. The final length of the mirror is 6.0 cm. The object is placed beyond the focal point, i.e p>i. What are the object and image distances p, and i? (Hint: obtain a quadratic equation to solve for p or i).Explanation / Answer
The focal length of the mirror is f = 6 cm As the image is real, the image and object or on the same side of the mirror Using the mirror equation 1/p + 1/i = 1/f P is the object distance i is the image distance f is the focallength As the image formed is 9.0 cm away from the object, and p>i p-i = 9 cm p = 9 + i Substitute this value into the mirror equation 1/9+i + 1/i = 1/6 i(9+i) = 6(9+2i) i^2 - 3i - 54 = 0 (i-9)(i+6) = 0 i = 9 cm or -6 cm As the image is real, i should be positive Therefore i = 9 cm The object distance p = 9 + 9 = 18 cm