Physics · Ch 6 — Optics
Angle of Deviation due to Reflection
Angle of Deviation due to Reflection
The angle of deviation is the angle between the incident ray's original direction and the direction the light ends up travelling in after reflection. Drawing the incident ray , the reflected ray , and the undeviated continuation of the incident ray , the deviation is the angle . Simple geometry ( in general) combined with the law of reflection gives for reflection at a plane surface. Equivalently, using the glancing angle measured between the incident ray and the mirror surface itself (rather than the normal), the same deviation works out to the tidier form . A related, important general result: if a plane reflecting surface is tilted through a small angle (with the incident ray held fixed), the reflected ray swings through twice that angle, -- a doubling effect exploited in sensitive optical-lever instr …
What this figure shows. Two related constructions. In (a), the incident ray AO continues undeviated as the imaginary line OC, while the actual reflected ray is OB; the angle between OB and OC is the deviation d, and simple geometry using i = r gives d = 180 degrees minus 2i. In (b), the same deviation is instead expressed using the glancing angle alpha measured between the incident ray and the plane mirror surface XY itself (rather than the normal), giving the equivalent, often more convenient, formula d = 2 alpha -- both formulas describe exactly the same physical dev …
Worked out. A reflecting surface AB carries an incident ray IO and reflected ray OR1, both making the equal angle i with the normal N (law of reflection). The surface is now tilted through a small angle theta to a new position A'B'; because the normal is always perpendicular to the surface, the new normal N' is also tilted by exactly theta. The incident ray IO is physically unchanged, but it now makes a new angle of incidence (i + theta) with the tilted normal, so by the law of reflection the new reflected ray OR2 also leaves at angle (i + theta) on the other side of N'. Comparing the original reflected direction OR1 with the new reflected direction OR2 by adding and subtracting these angles about the fixed line OR1 shows the reflected ray has swung through exactly (i + theta) minus (i - theta) = 2 theta. So tilting a mirror by any angle theta always swings the reflected ray through twice that angle, 2 theta -- a doubling effect used, for instance …