Sample Problems for The Law of Reflection

Important Information

When light is reflected from a surface, the angle of incidence is always equal to the angle of reflection, where both angles are measured from the path of the light to the normal to the surface at the point at which light strikes the surface.  This equality is known as the law of reflection.

Sample Problem 1:

Light is incident on a flat surface, making an angle of 10o with that surface, as shown in the figure to the right.  (a)  What is the angle of incidence?  (b)  What is the angle of reflection?  (c)  Sketch the path of the reflected beam on the diagram.
Light striking a surface at an angle of 10 degrees from the surface

Solution:

 
(a) If the light makes an angle of 10o with the surface, it makes an angle of 80o with the normal to the surface.  Thus the angle of incidence is 80o.
(b) According to the law of reflection, the angle of reflection equals the angle of incidence.  So the angle of reflection (measured to the normal) is 80o.
(c) The path of the light is shown in the figure below.
Light striking a surface at 80 degrees to the normal is reflected at 80 degrees to the normal.



 

Sample Problem 2:

Three initially parallel rays of light are incident at slightly different points on a bumpy surface, as indicated in the figure to the right.  The angles of incidence are 15o for ray A (blue in figure), 31o for ray B (green), and 47o for ray C (red).  (a)  What are the angles of reflection for the three rays?  (b) Will the three rays remain parallel after reflection?  (c)  Sketch the paths of the reflected rays on the diagram.
Three initially collimated rays strike a bumpy surface at different angles:  15 degrees, 31 degrees, and 47 degrees

Solution:

 
(a) According to the law of reflection, the angle of reflection must equal the angle of incidence for each ray.  Thus ray A will have an angle of reflection of 15o, B will have an angle of reflection of 31o, and the third will have an angle of reflection of 47o.
(b) No; the three rays will diverge after reflection.  The divergence is due not only to the differences in the angles of reflection, but also to the differences in the directions of the normal at each incident point.
(c) The figure below roughly indicates the paths of the three rays after reflection, illustrating the divergence.  The blue ray is reflected through an angle of 30° from the initial path, the green ray is reflected through 62°, and the red ray is reflected through a whopping 94° as compared to the initial path!
The three initially collimated rays are scattered by a bumpy surface, leaving the surface in different directions.

This sample problem illustrates diffuse reflection, discussed on the next content page.
 

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