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11.A 9cm long object is placed at 90cm from a spherical mirror perpendicular to its principal axis. A real imageis formed at 30cm from the mirror. What is the radius of curvature of the mirror? {Ans: - 45 cm)

Answer»

Height of object ho = 9 cm

Focal lenght of convex lens = ? cm

Object distance u = -90 cm

Image distance v = 30 cm

Image height hi = ?

Lens formula: 1/v - 1/u = 1/f

1/f = 1/v - 1/u

= 1/30 + 1/(-90)

= -1/45

⇒ v = - 45 cm

The image distance is 45 cm on the same side of the lens as the object.

Magnification m = v/u = (-45)/(-90) = 1/2 = hi/ho = hi/9

⇒ hi = 9/2 cm



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