The questions states: The radius of curvature of a mirror is24cm. A ring is plac

Question

The questions states: The radius of curvature of a mirror is24cm. A ring is placed in front of the mirror. Theimage is twice the size of the ring. From this I know that f = 12cm, and the mirror must beconcave. But what I can't figure out is how to calculate thetwo possible object distances of the ring given r and f. Cananyone point me to the correct equation. I wanted to use themirror equation but I do not know di.

Thanks for any help. The questions states: The radius of curvature of a mirror is24cm. A ring is placed in front of the mirror. Theimage is twice the size of the ring. From this I know that f = 12cm, and the mirror must beconcave. But what I can't figure out is how to calculate thetwo possible object distances of the ring given r and f. Cananyone point me to the correct equation. I wanted to use themirror equation but I do not know di.

Thanks for any help.

Explanation / Answer

.    Radiusof curvature (R) = 24 cm .    ==> Focal length (f) = R / 2 = 12 cm .    Magnification (M) = - v / u = 2 .    ==> v = - 2 u ; Where u = Object distance ; v = Image distance . From Lens Maker's formula we have : .    1 / f = 1 / u + 1 / v .    ==> 1 / 12 = 1 / u - 1 / 2u .    ==> 1 / 12 = 1 / u [ 1 - (1 /2) ] .    ==> 1 / 12 = 0.5 / u .    ==> u   = 0.5 * 12 = 6 cm . Hence Object distance (u) = 6 cm . Hope this helps u!

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