Question

A person looks at her image in a shiny spherical decoration when her face is 30 cm from the surface of the decoration. the diameter of decoration is 20cm. find the position of image.​

Answer 1

Answer:

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Answer 2

Given: A person looks at her image in a shiny spherical decoration when her face is 30 cm from the surface of the decoration. The diameter of the decoration is 20 cm.

To find: The position of the image.​

Solution:

• Since the diameter of the decoration is 20 cm, its radius can be calculated as,

        $radius = \frac{diameter}{2}$

                    $= \frac{20}{2}$

                    $= 10 cm$

• The focal length of the shiny surface can be calculated as,

        $f = \frac{R}{2}$

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

        $f = \frac{10}{2}$

           $= 5 cm$

• The position of the image formed by a mirror can be found by 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 shiny spherical decoration.

        $\frac{1}{v} + \frac{1}{30 cm} = \frac{1}{5 cm}$

        $\frac{1}{v} = \frac{5}{30}$

        $v = 6 cm$

Therefore, the position of the image is 6 cm from the decoration.