Question on reflection of light

Hi everyone,

Apologies in advance if this is the wrong place to post this.

I'm currently struggling with a question and am hoping that someone here can kindly shed some light.

A man stands in the middle of a room 17m wide and looks into a mirror on one
wall of the room. What dimensions must the mirror have in order that he can just
see the image of a rectangular patch on the opposite wall of size 7m × 4m?

I know the answer to this, but am struggling to illustrate my answer in terms of equations. Does anyone know the formulas I need to use?

Thanks in advance.

Quote:

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Originally Posted by Josh31

Hi everyone,

Apologies in advance if this is the wrong place to post this.

I'm currently struggling with a question and am hoping that someone here can kindly shed some light.

A man stands in the middle of a room 17m wide and looks into a mirror on one
wall of the room. What dimensions must the mirror have in order that he can just
see the image of a rectangular patch on the opposite wall of size 7m × 4m?

I know the answer to this, but am struggling to illustrate my answer in terms of equations. Does anyone know the formulas I need to use?

Thanks in advance.

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2.3333...m x 1.3333...m, PM for formulas and explanation. There is a simple explanation that applies to this scenario and a more advanced catoptric formula that will come up later when the mirror has curvature (catoptric power).

Attachment 14328Presuming it's a flat mirror, it's the "law of reflectance" which is "angle of incidence = angle of reflectance".

Draw a diagram and do a "ray trace" from the bottom and top of the mirror, include the distance, put an "eye" in the middle of the diagram, and use trigonometry and you'll get the answer.

You have to make a few assumptions, such as the mirror is centered above and below the eye.

The ray trace will look kind of like a "W" turned on it's side and the eyeball at the middle peak (which will be actually half the length of the legs, unlike the "w" I just typed) and the lower peaks will be the upper and lower edges of the mirror, and the top of the "W" lines will represent the upper and lower edges of the "patch of wall".

(DANG IT, I'LL DRAW AND ATTACH at top, blue is mirror, red is patch)

The answer will be half the size of the patch, if I'm right.

Drk, right on man, except look at the legs of your W if the path traveled through the mirror is through the legs of the W, the person in the middle would have one small leg to travel through to the mirror, then one small leg to travel back, and another small leg to get to the patch, that's 3 small legs of travel, so the answer will be a third (1/3).

Ah so. Thanks.