Question

an object is placed at 30cm in front of a convex mirror of focal length 15cm .the object is shifted away by 10cm. what will the shift in image position be

Answer 1

U=30, F=15.
Find v= ??
Then ,U= 10
We can find v easily.

Answer 2

Initially..
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F = 15 cm
U = - 30 cm
V =?
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ or. \: \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \\ or. \: \frac{1}{v} = \frac{1}{15} - ( \frac{1}{ - 30} ) \\ or. \: \frac{1}{v} = \frac{2 + 1}{30} = \frac{1}{10 } \\ so \: \: v = 10cm$
Final
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U = - 40 cm
F =15 cm
V =?

$\frac{1}{v} = \frac{1}{f} - \frac{1}{u } \\ or. \: \frac{1}{v} = \frac{1}{15} - ( - \frac{1}{40} ) \\ or. \: \frac{1}{v} = \frac{8 + 3}{120} = \frac{11}{120} \\ or. \: v = \frac{120}{11} = 10.9 \: cm$
So ..
Shift in image position = Final image position - initial image position
=10.9 - 10 = 0.9 cm
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