Reflection On A Plane Mirror

What is Reflection of Light?

When the light ray falling from the object on the surface bounces back are known as reflected rays and this phenomenon is known as a reflection of light.

What are Laws of Reflection?

The laws of reflection are divided into two main points and they are:

  • The angle of incidence is equal to the angle of reflection.
  • The incident ray, reflected ray, and the normal at the point of incidence, all lie in the same plane.

What is Reflection on a Plane Mirror?

When the light rays which gets stroked on the flat mirror and gets reflected back. According to laws of reflection, the angle of reflection is equal to the angle of incidence. The image is obtained behind the plane which is present in the mirror. This process of obtaining a mirror image which virtual and erect is known as a reflection on a plane mirror.

Characteristics of Image formed by Plane Mirror

Following are the characteristics of image formed by plane mirror:

  • The image obtained by the plane mirror is always erect and virtual.
  • The image size and the size of the object, both are equal.
  • The distance between the image obtained is as the distance at which the object is placed.
  • Laterally inverted images are obtained.

Types of Reflection

Following are the three types of reflection of light:

  • Mirror reflection
  • Specular reflection
  • Diffuse reflection

Types of reflection

Image Formed by the Plane Mirror

Consider the light rays 1, 2 and 3 shown by solid lines. The wavefronts which are perpendicular to these light rays are shown by the thin lines. The secondary wavefronts generated are the circular fronts described.

At point a, a wavefront is generated due to the secondary source on ray 2. At the same time, other wavefronts are generated at points c and b. Since wavefronts at points, a and b are generated at the same time ac = cb. Thus the triangle acb is isosceles and the angles θ1 = θ2.

Note that θ1 is the angle of incidence and θ2 is the angle of reflection.

Thus, Angle of incidence = Angle of reflection

Below is the image formed by the plane mirror

Image formed by the plane mirror

Image formed by the plane mirror

Related Article:

Huygens Principle and Law of  Refraction

Huygens Principle and Law of Refraction

Refraction of a wavefront

Consider the light rays 1, 2 and 3 shown by solid lines refracted to rays 1’, 2 and 3’ respectively. The wave fronts which are perpendicular to these light rays are shown by the thin lines. Consider the wave fronts to be one wavelength apart in their respective media where refractive indices n1 < n2.  The incident angle is θ1 and the refracted angle is θ2.  Consider the wave front at c, the front is bent in the new medium because the speed of light is slower. However, since the frequency of the waves are a constant, the wavelengths change across media to accommodate the change in speed.

i.e.,

\(ϑ_1\) = \(ϑ_2\)

\({v_1}{λ_1}\) = \({v_2}{λ_2}\)

Also from figure the side ac is common to the triangles abc and adc,

\(ac\) = \(ac\)

\(\frac{bc}{sinθ_1}\) = \(\frac{ad}{sinθ_2}\)

But the line segments ac and ad represent the wavelengths in their respective media,

\(\frac{λ_1}{sinθ_1}\) = \(\frac{λ_2}{sinθ_2}\)

\(\frac{v_1}{sinθ_1}\) = \(\frac{v_2}{sinθ_2}\)

\(\frac{sin~ θ_1}{sin~θ_2}\) = \(\frac{v_1}{v_2} \)

\(\frac{sin~θ_1}{sin~θ_2}\) = \(\frac{\frac{c}{v_2}}{\frac{c}{v_1}}\) = \({n_2}{n_1} \)

Where, c is the speed of light in vacuum.

Thus, the Huygens principle can be used to prove the law of refraction. A similar exercise can be conducted for n1 > n2.

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