Q.Four times magnified image of any object is produced at 9 cm distance on a screen from the object by spherical mirror. Calculate the focal length of the mirror.
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Start your 14-day free trial to unlock the full solution →A 4x magnified real image on a screen means |v| = 4|u|; since the object-to-screen distance is v - u = 9 cm, we get u = 3 cm and v = 12 cm, and the mirror formula gives a concave mirror of focal length 2.4 cm.
Given: magnification magnitude |m| = 4, and the image is real (formed on a screen), hence inverted, so m = -4. The object and screen are 9 cm apart.
Step 1 - Magnification relation: m = -v/u = -4, so |v| = 4|u|.
Step 2 - Geometry: for a concave mirror the object and its real image lie on the same side, so the object-to-screen distance is |v| - |u| = 9 cm. Then 4|u| - |u| = 3|u| = 9 cm, giving |u| = 3 cm and |v| = 12 cm.
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