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Ray Optics And Optical Instruments

Question
CBSEENPH12047703

A short linear object of length b lies along the axis of a concave mirror of focal length ' f ' at a distance 'u' from the pole of the mirror, what is the size of image?

  • fu-f b

  • fu-f2 b

  • fu-f b2

  • fu-f

Solution

B.

fu-f2 b

Using the relation for the focal length of concave mirror

1f = 1u+1ν         ...1 Differentiating equation (1) we get0 = -1ν2dv -1u2du    =-ν2u2×b                  (here :- du =b)From equation (1)1ν=1f-1u =u-ff uor uv =u-ffvu=fu-fNow from equations (2) and (3) we getdv =-fu-f 2 b

size or image is=fu-b2b