PLEASE ANSWER WILL QUICKLY RATE THE CORRECT ANSWER THE REAL

PLEASE ANSWER, WILL QUICKLY RATE THE CORRECT ANSWER

THE REAL QUESTION THAT NEEDS TO BE ANSWERED IS AT THE BOTTOM OF THE POST, BELOW THE EXAMPLE QUESTION AND THE EXAMPLE QUESTION\'S SOLUTION>>>

EXAMPLE QUESTION W/ SOLUTION: Use this as a reference

Let’s consider the image formed by a shiny spherical Christmas ornament. Santa checks himself for soot by looking at his reflection in a silvered Christmas tree ornament 0.750 m away (Figure 1) . The diameter of the ornament is 7.20 cm. Let’s estimate Santa’s height as 1.6 m. Where and how tall is the image of Santa formed by the ornament? Is it upright or inverted?

Figure 2

Figure 1

SOLUTION

SET UP (Figure 2) shows our diagram. (To limit its size, we drew it not to scale; the angles are exaggerated, and Santa would actually be much taller and farther away.) The surface of the ornament closest to Santa acts as a convex mirror with radius R=?(7.20cm)/2=?3.60cmand focal length f=R/2=?1.80cm. The object distance is s=0.750m=75.0cm.

SOLVE From 1/s+1/s?=1/f,

1s?s?==1f?1s=1?1.80cm?175.0cm?1.76cm

The lateral magnification m is given by the following:

m=y?y=?s?s=??1.76cm75.0cm=2.35×10?2

Because m is positive, the image is upright, and it is only about 0.0235 as tall as Santa himself. Thus, the image height y? is

y?=my=(0.0235)(1.6m)=3.8×10?2m=3.8cm

REFLECT The object is on the same side of the mirror as the incoming light, so the object distance s is positive. Because s\' is negative, the image is behind the mirror—that is, in (Figure 2) it is on the side opposite to that of the outgoing light—and it is virtual. The image is about halfway between the front surface of the ornament and its center. Thus, this convex mirror forms an upright, virtual, diminished, reversed image. In fact, when the object distance s is positive, a convex mirror alwaysforms an upright, virtual, diminished, reversed image.

---------------------------------------------------------------------------

ACTUAL QUESTION: Please Answer

Part A:

One of Santa’s elves scoots in halfway between Santa and the ornament to check and see that his hat is on straight. His image height in the ornament is 3.00 cm . What is the height of the elf?

Express your answer in centimeters to three significant figures.

Solution

The ornament is a convex mirror with

f= 1.8 cm

the formula of image formation with a spherical mirror is

1/u +1/v = 1/f

The convention is to measure distances from the pole of the mirror as origin and +ve x to the right

f = 1.8

u = -37.5 cm, elve is half way between Santa and the mirror

-1/37.5 +1/v = 1/1.8

v = 1.8*37.5/(37.5+1.8) = 1.72

magnification m = v/u = 1.72/37.5

image height = 3 cm

object height = 3.0 * 37.5/1.72 = 65.41 cm