Show that the image formed in a plane mirror is as far behind the mirror as the object is in front
Show that the image formed in a plane mirror is as far behind the mirror as the object is in front
Consider an object A placed in front of a mirror M.
A ray AD from A incident normally on the mirror at D is reflected back along DA.
The Ray AO is reflected along OB and appears to come from point I behind the mirror.
The intersection I of the rays AD and BO is the image position.
From above angles,
x = i (alternating angles)
i = r (2nd law of reflection)
r = y (corresponding angles)
Combining all the equations gives
x = i = r = y
Þ angle x = angle y
Tan x = tan y
DO/AD = DO/ID
Thus AD = ID.
Therefore, the image is as far behind the mirror as the object is in front
Thank you
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