A ray of light is incident on a plane mirror at an angle of 40° with respect to a surface normal. When it gets reflected from the mirror it undergoes a deviation of
100°
Understanding Light Reflection and Deviation on a Plane Mirror
When a ray of light strikes a plane mirror, it bounces back into the same medium. This phenomenon is called reflection. The reflection of light from a plane mirror follows the laws of reflection.
Key Concepts: Angle of Incidence and Angle of Reflection
- Normal: An imaginary line perpendicular to the surface of the mirror at the point where the incident ray strikes.
- Angle of Incidence (\(\theta_i\)): The angle between the incident ray and the normal.
- Angle of Reflection (\(\theta_r\)): The angle between the reflected ray and the normal.
Law of Reflection
The Law of Reflection states two main points:
- The angle of incidence is equal to the angle of reflection (\(\theta_i = \theta_r\)).
- The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
Calculating the Deviation Angle
The deviation angle is the angle through which the incident ray turns as a result of reflection. It is the angle between the original direction of the incident ray and the direction of the reflected ray.
Given in the question, the angle of incidence (\(\theta_i\)) is 40° with respect to the surface normal.
According to the Law of Reflection, the angle of reflection (\(\theta_r\)) is equal to the angle of incidence.
So, \(\theta_r = \theta_i = 40^\circ\).
Consider the path of the incident ray and the reflected ray. If the mirror were not present, the incident ray would continue in a straight line. The deviation is the angle between this straight line (the original path) and the reflected ray.
The angle between the incident ray and the reflected ray is the sum of the angle of incidence and the angle of reflection, which is \(\theta_i + \theta_r\). This angle is measured at the point of incidence, between the two rays.
Angle between incident and reflected ray \(= 40^\circ + 40^\circ = 80^\circ\).
The incident ray, the normal, and the reflected ray lie in a plane. The direction of the incident ray and its extension form a straight line (180°). The angle between the incident ray's original path (extended straight line) and the reflected ray is the deviation angle.
Deviation angle (\(\delta\)) \(= 180^\circ - (\theta_i + \theta_r)\)
Since \(\theta_i = \theta_r\), this can also be written as:
Deviation angle (\(\delta\)) \(= 180^\circ - 2\theta_i\)
Using the given angle of incidence (\(\theta_i = 40^\circ\)):
Deviation angle (\(\delta\)) \(= 180^\circ - 2(40^\circ)\)
Deviation angle (\(\delta\)) \(= 180^\circ - 80^\circ\)
Deviation angle (\(\delta\)) \(= 100^\circ\)
Therefore, the reflected ray undergoes a deviation of 100° from the original path of the incident ray.
Summary of Calculation
| Parameter | Value |
|---|---|
| Angle of Incidence (\(\theta_i\)) | 40° |
| Angle of Reflection (\(\theta_r\)) | 40° (by Law of Reflection) |
| Angle between Incident and Reflected Ray (\(\theta_i + \theta_r\)) | \(40^\circ + 40^\circ = 80^\circ\) |
| Deviation Angle (\(\delta = 180^\circ - (\theta_i + \theta_r)\)) | \(180^\circ - 80^\circ = 100^\circ\) |
Conclusion on Light Deviation
For a ray of light incident on a plane mirror at an angle of 40° with respect to the normal, the angle of reflection is also 40°. The total deviation experienced by the ray is the angle it turns from its original path, which is calculated as 180° minus the sum of the angles of incidence and reflection. This results in a deviation of 100°.
Revision Table: Light Reflection from Plane Mirror
| Concept | Definition/Formula |
|---|---|
| Angle of Incidence (\(\theta_i\)) | Angle between incident ray and normal |
| Angle of Reflection (\(\theta_r\)) | Angle between reflected ray and normal |
| Law of Reflection | \(\theta_i = \theta_r\); Rays & normal are coplanar |
| Deviation Angle (\(\delta\)) | Angle between original incident direction and reflected direction |
| Formula for Deviation | \(\delta = 180^\circ - 2\theta_i\) (for plane mirror) |
Additional Information: Reflection Concepts
Understanding reflection from a plane mirror is fundamental in optics. Here are a few related points:
- Virtual Image: A plane mirror forms a virtual, erect, and laterally inverted image of an object. The image distance is equal to the object distance.
- Multiple Reflections: When light reflects off two or more mirrors, multiple images can be formed. The number of images depends on the angle between the mirrors. For two mirrors placed at an angle \(\theta\), the number of images is generally given by \(\frac{360^\circ}{\theta} - 1\) (if \(\frac{360^\circ}{\theta}\) is an integer and the object is not on the angle bisector).
- Uses of Plane Mirrors: Plane mirrors are used in periscopes, kaleidoscopes, as dressing mirrors, and in various optical instruments.
- Angle with the Surface: Sometimes, the angle of incidence is given with respect to the mirror surface, not the normal. If the angle with the surface is \(\alpha\), then the angle of incidence \(\theta_i = 90^\circ - \alpha\). Pay close attention to how the angle is defined in the problem.
In this problem, the angle was given with respect to the normal, simplifying the application of the law of reflection and the deviation formula.
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