A spherical glass ornament is 7.00 cm in diameter. An object is placed 11.8 cm away from the...

Question:

A spherical glass ornament is {eq}7.00\ cm {/eq} in diameter. An object is placed {eq}11.8\ cm {/eq} away from the ornament.

a) Where will its image form?

b) What is the magnification of the image?

Convex mirror:

The mirrors that converge the light are known as the convex or the converging mirror. The focal length of the convex mirror is negative and the image distance, object distance are related with the mirror formula.

Given Data:

• Radius of the spherical glass {eq}\rm (R) = 3.5 \ cm {/eq}
• Object distance from the mirror {eq}\rm (u) = 11.8 \ cm {/eq}

Now, the focal length of the mirror would be

{eq}\rm f = \dfrac{-R}{2} \\ f = \dfrac{-3.5}{2} \\ f = -1.75 \ cm {/eq}

(a)

Now, using the mirror formula

{eq}\rm \dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f} \\ \dfrac{1}{11.8} + \dfrac{1}{v} = \dfrac{-1}{1.75} \\ v = -1.524 \ cm {/eq}

(b)

Now, the magnification of the image

{eq}\rm m = \dfrac{-v}{u} \\ m = \dfrac{-(-1.1524)}{11.8} \\ m = 0.129 {/eq}