Question

a rod of length 10 centimetres life along the principal axis of concave mirror of focal length 10cm in such a way that the ender and closer to the pole is 20 CM away from it the length of the image is

Answer 1

ANSWER:

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Given: A rod of length 10cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. 

To find the length of the image

Solution:

As per the given criteria,

Focal length of the concave mirror, f = -10cm

Object distance at point A, u= - 20cm
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Applying the mirror formula, we get

$\frac{1}{u} + \frac{1}{v} = \frac{1}{f} \\ = > \frac{1}{v} = \frac{1}{( - 10)} - \frac{1}{ (- 20)} \\ \frac{1}{v} = \frac{ - 2 + 1}{20} \\ v = 20cm........(1)$

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Object distance at B,


$u = - 20 + 10 = - 30cm \\ applying \: the \: mirror \: formula \: we \: get \\ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \frac{1}{v} = \frac{1}{( - 10)} - \frac{1}{( - 30)} \\ \frac{1}{v} = \frac{ - 3 + 1}{30} \\ v = 15cm ........(2)$
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So length of the image is,

$= v1 - v2 \\ = 20 - 15 \\ = 5cm$
Therefore,
the length of the image formed will be 5cm.

Answer 2

a rod of length 10 centimetres life along the principal axis of concave mirror of focal length 10cm in such a way that the ender and closer to the pole is 20 CM away from it the length of the image is