Results 1 to 5 of 5

Thread: Question on reflection of light

  1. #1
    OptiBoard Novice
    Join Date
    May 2019
    Location
    UK
    Occupation
    Optical Retail
    Posts
    1

    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.

  2. #2
    Master OptiBoarder MakeOptics's Avatar
    Join Date
    Aug 2011
    Location
    none
    Occupation
    Other Eyecare-Related Field
    Posts
    1,325
    Quote Originally Posted by Josh31 View Post
    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.
    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).
    http://www.opticians.cc

    Creator of the industries 1st HTML5 Browser based tracer software.
    Creator of the industries 1st Mac tracer software.
    Creator of the industries 1st Linux tracer software.

  3. #3
    What's up? drk's Avatar
    Join Date
    Mar 2004
    Location
    Ohio
    Occupation
    Optometrist
    Posts
    7,729
    Click image for larger version. 

Name:	Untitled.png 
Views:	7 
Size:	23.1 KB 
ID:	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.
    Last edited by drk; 06-12-2019 at 10:30 AM.

  4. #4
    Master OptiBoarder MakeOptics's Avatar
    Join Date
    Aug 2011
    Location
    none
    Occupation
    Other Eyecare-Related Field
    Posts
    1,325
    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).
    http://www.opticians.cc

    Creator of the industries 1st HTML5 Browser based tracer software.
    Creator of the industries 1st Mac tracer software.
    Creator of the industries 1st Linux tracer software.

  5. #5
    What's up? drk's Avatar
    Join Date
    Mar 2004
    Location
    Ohio
    Occupation
    Optometrist
    Posts
    7,729
    Ah so. Thanks.

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Replies: 0
    Last Post: 04-07-2015, 09:04 PM
  2. AR Reflection Colors
    By D_Zab in forum General Optics and Eyecare Discussion Forum
    Replies: 5
    Last Post: 02-11-2015, 01:40 PM
  3. For reflection
    By Shwing in forum Just Conversation
    Replies: 9
    Last Post: 11-01-2004, 06:42 AM
  4. For More Reflection
    By Shwing in forum Just Conversation
    Replies: 0
    Last Post: 10-29-2004, 10:35 PM
  5. AR REFLECTION
    By tmtaylo in forum Ophthalmic Optics
    Replies: 5
    Last Post: 12-10-2000, 05:23 AM

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
OptiBoard is proudly sponsored by:
Younger Optics and Vision Equipment