Question

The glancing angle of incidence is \[{{10}^{\text{o}}}\]. What will be the glancing angle of reflection?
A. \[{{10}^{\text{o}}}\]
B. \[{{80}^{\text{o}}}\]
C. \[{{170}^{\text{o}}}\]
D. \[{{60}^{\text{o}}}\]

Answer 1

Hint: By law of reflection, when a ray of light is incident on a surface, the angle of incidence is equal to the angle of reflection.

Complete step by step answer:
The glancing angle of incidence is the angle between the incident beam and the surface. The glancing angle of incidence is complement to the angle of incidence.
The glancing angle of incidence, \[\angle i'={{10}^{\text{o}}}\]
As the glancing angle of incidence is complement of the angle of incidence \[\angle i\], so
\[\begin{gathered}
  & \angle i+\angle i'={{90}^{\text{o}}} \\
 & \angle i={{90}^{\text{o}}}-\angle i' \\
 & \angle i={{90}^{\text{o}}}-{{10}^{\text{o}}}={{80}^{\text{o}}} \\
\end{gathered}\]
By law of reflection of light,
\[\angle i=\angle r\], where \[\angle i\] denotes the angle of incidence and \[\angle r\] denotes the angle of reflection.
So, \[\angle i=\angle r={{80}^{\text{o}}}\]
Therefore, the angle of reflection is \[{{80}^{\text{o}}}\].
The glancing angle of reflection is complement to the angle of reflection.
Therefore, the glancing angle of reflection \[\angle r'\] is
\[\begin{gathered}
  & \angle r'={{90}^{\text{o}}}-\angle r \\
 & \angle r'={{90}^{\text{o}}}-{{80}^{\text{o}}}={{10}^{\text{o}}} \\
\end{gathered}\]

So, the correct answer is “Option A”.

Additional Information:
The angle of incidence is the angle between the incident beam and the normal, drawn perpendicular to the surface at the point of incidence.
The angle of incidence is the angle between the reflected beam and the normal, drawn perpendicular to the surface at the point of incidence.
By law of reflection, “the incident ray, the reflected ray and the normal to the surface at the point of incidence, all lie in the same plane”.

Note:
As the angle of incidence is equal to the angle of reflection, so the complement of the angle of incidence is equal to the complement of the angle of reflection, that is, the glancing angle of incidence is equal to the glancing angle of reflection.