Question

A guy named Joe, who is 1.6 meters tall, enters a room in which someone has placed a large convex mirror with radius of curvature RRR equal to 30 meters. The mirror has been cut in half, so that the axis of the mirror is at ground level. (Figure 1)As Joe enters the room, he is 5 meters in front of the mirror, but he is looking the other way, so he fails to see it. When he turns around, he is startled by his own image in the mirror. Figure 1 of 2The figure shows a man standing on a horizontal x-axis in front of a vertical mirror. The mirror is convex.

Part A How far away does the image appear to Joe? Express your answer in meters, to three significant figures or as a fraction. View Available Hint(s) mm SubmitPrevious Answers Incorrect; Try Again; 7 attempts remaining This is the image distance (i.e., the distance from the mirror to the image). You want the distance from Joe to the image, so you must combine this distance with Joe's distance from the mirror. Should you add or subtract? Part B What is the image height yimyimy_im that Joe sees in the mirror? Express your answer in meters, to three significant figures or as a fraction. View Available Hint(s) yimyimy_im = nothing mm Submit Joe is so startled by his image that he falls forward. (Assume that his feet stay at the same position.)(Figure 2) Part C Now what is the length (i.e., the distance from head to toe) of Joe's image? Express your answer in meters, to three significant figures or as a fraction. View Available Hint(s) nothing mm Submit Provide Feedback Next

Incorrect. Incorrect; Try Again; 7 attempts remaining. Feedback. This is the image distance (i.e., the distance from the mirror to the image). You want the distance from Joe to the image, so you must combine this distance with Joe's distance from the mirror. Should you add or subtract? End of feedback.

Answer 1

Solution of Part A:

Here,
Radius of curvature of the mirror
Object distance from the center of the mirror or Joe's real position
Image distance from the center of the mirror or Joe's position in the mirror
Object height or Joe's height
Image height or Joe's height

Focal length of the convex mirror:

Now, according to mirror formula:

Therefore, the image of Joe is virtual inside the mirror at 3.75 m from the center of the mirror.

Now, to Joe, the image will appear at the distance

Therefore, to Jo, his image appears at 8.75 m from where he is standing.

NOTE: Negative sign in image distance indicates that Joe's image is virtual inside the mirror.

Solution of Part B:

According to mirror magnification formula

Therefore, Joe's image height is 1.20 m.

Solution of Part C:

Joe is so startled by his image that he falls forward that means he is decreasing his head's distance from the mirror while his feet stay at the same position.

That means Joe's head now at the distance from the image inside the mirror.

Now, according to mirror formula, the image distance from the center of the mirror to his image:

Now, the length of the Joe's image is given by

Therefore, the Joe's image length is now 0.98 m.