If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be :
Question
If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be :
Solution
To solve this problem, we can use the mirror formula which is 1/f = 1/v + 1/u.
Given that the magnification is -2 (it's negative because the image is virtual), we can say that the image distance (v) is -2 times the object distance (u).
Also, we know that the distance between the object and the image is 15 cm. So, we can write the equation as u - (-2u) = 15 cm. Solving this gives u = 5 cm.
Now, we can substitute u = 5 cm and v = -2u = -10 cm into the mirror formula.
So, 1/f = 1/-10 + 1/5 = -1/10 + 2/10 = 1/10.
Therefore, the focal length f = 10 cm.
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