Question

4. A mirror is part of sphere of diameter 9.3 cm. A boy stands 0.5 m away from the mirror
and is amused to see his image. Determine the height of the boy's image if he is 1.3 m
tall. Where does the boy find his image? Why do you think the boy is so amused at
seeing his image? (A ray diagram is required).​

Answer 1

A) Distance of the image: -4.25 cm (virtual)

B) Height of the image: 0.11 m (upright)

C) The boy is amused because his image is smaller than his real size (see attached ray diagram)

Explanation:

A-B)

The mirror is part of a sphere: this means that it is a convex (diverging) mirror.

The radius of this mirror is half of the diameter:

$f=\frac{r}{2}=\frac{9.3}{2}=4.65 cm$

The focal length of a convex mirror is negative, so

$f=-4.65 cm$

We can now use the mirror equation to find the distance of the image from the mirror:

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$

where

p = 0.5 m = 50 cm is the distance of the boy from the image

Solving for q, we find:

$\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-4.65}-\frac{1}{50}=-0.235\\q=\frac{1}{-0.235}=-4.25 cm$

And the negative sign means the image is virtual.

B)

Now we can fidn the height of the boy by using the magnification equation:

$M=\frac{y'}{y}=-\frac{q}{p}$

where

y = 1.3 m is the height of the boy

y' is the height of the image

Solving for y',

$y'=-\frac{qy}{p}=-\frac{(-4.25 cm)(1.3 m)}{50 cm}=0.11 m$

And the positive sign means the image is upright.

C)

The boy is amused because his image in the mirror is much smaller than his real height, and therefore distorted.

In fact, his real height is 1.3 m, while his image in the mirror is only 0.11 m.

This fact can be verified by looking at the ray diagram in attachment. The ray diagram is built by drawing a ray of light going from the top of the boy to the mirror (parallel to the axis), and then being reflected towards the focal point. Then anoter ray of light goes straight from the top of the boy towards the center of curvature of the mirror.

The resulting image is located at the intersection point between the two rays, and here it is labelled with the letter q.

Learn more about mirrors:

brainly.com/question/8737441

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