Question

a 3.0 tall object is 20.0 cm from a 16.0 radius concave mirror determine the image position and image height


answer:-

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Answer 1

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Answer 2

Given: A 3 cm tall object is 20 cm from a 16 cm radius concave mirror.

To find: The image position and the image height.

Solution:

• The focal length of a concave mirror can be calculated as,

        $f = \frac{R}{2}$

• Here, R is the radius and f is the focal length.

           $= \frac{16 cm}{2}$

           $= 8 cm$

• The position of the image formed by the concave mirror can be calculated using the formula,

        $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

• Here, v is the distance of the image formed and u is the distance of the object from the concave mirror.

        $\frac{1}{v} + \frac{1}{20 cm} = \frac{1}{8 cm}$

        $\frac{1}{v} = \frac{6}{80}$

        $v = \frac{40}{3} cm$

           $= 13.33 cm$

• Let the object height be o and the image height be i, then the height of the image can be calculated as,

        $\frac{i}{o} = \frac{v}{u}$

        $\frac{i}{3} = \frac{\frac{40}{3} }{20}$

       $i = 2 cm$

Therefore, the image position is 13.33 cm from the mirror and its height is 2cm.