Two mirrior are kept perpendicular to each
Other. A ray strikes one mirror ate an angle
of 45° to Ehe normal. Find the angle of reflection
of the ray after reflection by the second
mirror, by drawing A ray diagram
Answers
Concepts used -
=> The basic concept of reflection is used here -
- Reflection is the bouncing back of light back into the same medium -
- when a light ray strikes a reflecting surface such as a mirror.
=> The laws of reflection are also used here -
- The angle of incidence is the angle formed between the normal and the incident ray, the angle of reflection is the angle formed between the reflected ray and the normal.
- The angle of incidence (i) is always equal to the angle of relection(r)
=> Also, the normal is a perpendicular drawn to the point where the incident ray strikes the reflecting surface.
=> Sum of angles in a triangle is 180 degrees.
=> Complementary angles are a pair of angles having a sum of 90 degrees.
Steps involved -
1) We draw the diagram with two mirrors at an angle of 90 degrees with each other, we have to silver the other side of each mirror and mark the angle between them as 90 degrees.
2) Now we show the incident ray falling at an angle of incidence of 45 degrees on the base mirror (or the upper mirror) we also show the normal at the point of incidence.
3) Now, using the law of reflection, we know that ∠i = ∠r = 45 degrees
=> So, the angle of reflection will also be 45 degrees from the first reflection, we show this in the diagram.
4) The normal makes an angle of 90 degrees with the mirror, so the two angles formed by the incident ray and the normal and the reflected ray and the normal are complementary angles, if one is 45 degrees the other will also be 45 degrees.
=> So the angles formed between the incident ray and the mirror is also 45 degrees and so is the angle formed between the reflected ray and the mirror, we mark this in the diagram.
5) We extend the first reflected ray until it strikes the second mirror.
=> The first reflected ray becomes the incident ray for the second mirror.
6) We draw a normal for the second incident ray on the second mirror as well.
7) We observe that the first reflected ray and the two mirror surfaces form a right angled triangle, 2 of the angles are 90 and 45 degrees, the other angle will be (180-90-45) = (90-45) = 45 degrees as well.
=> Thus, the second angle of incidence will be :
measure of normal - measure of angle between 2nd incident ray and 2nd mirror surface
i.e. 90 - 45 => 45 degrees.
8) We mark the second angle of incidence (45 degrees) and also draw the second reflected ray at an angle of reflection of 45 degrees with the normal (from the law of reflection - ∠i = ∠r = 45 degrees)
=> We mark the angle between the 2nd reflected ray and the 2nd mirror surface as 45 degrees (complementary angles - 90-45 = 45 degrees)
9) Lastly, we label all the points with random letters and complete the diagram.
Answer -
=> After following the steps and drawing the diagram, we get the angle of reflection of the ray from the second mirror as 45 degrees.
Refer to -
=> The diagram is as an attachement.
Answer is in the attachment
Tip : no used to measure the angles and make
