Reflection of Light Notes

Lesson 1: Reflection of Light

Focus Question

• Why does light reflected from a mirror make an image while light reflected from a piece of paper does not?

Objective

• IWBAT understand and apply the law of reflection to solve problems.
• Understand the properties of flat mirrors.

Keywords

• Specular Reflection
• Diffuse Reflection
• Plane Mirror
• Object
• Image
• Virtual Image

The Law of Reflection

• The law of reflection states the angle of incidence is equal to the angle of reflection.
• This applies to both smooth and rough surfaces.

Specular Reflection

• Specular reflection is caused by a smooth surface, in which parallel light rays are reflected in parallel.

Diffuse Reflection

• Diffuse reflection is caused by the scattering of light off a rough surface.

Example Problem

• A light ray strikes a plane mirror at an angle of $15^\circ$ to the normal. The mirror then rotates $20^\circ$ around the point where the beam strikes it so that the ray’s angle of incidence increases. The axis of rotation is perpendicular to the plane of the incident and to the reflected rays. What is the final angle of reflection of the light ray?
  • Known:
    • $\theta_{i, initial} = 15^\circ$
    • $\Delta\theta_{mirror} = 20^\circ$
  • Unknown:
    • $\theta_{r, final} = ?$
  • Determine the final angle of incidence.
  • Use the law of reflection to determine the final angle of reflection.
  • By rotating the mirror $20^\circ$, the angle of incidence and the angle of refraction were both increased by $20^\circ$.

Task Problems

• A light ray strikes a plane mirror at an angle of $25^\circ$ to the normal. The mirror is then rotated $15^\circ$ around the point where the beam strikes it, increasing the angle of incidence. The axis of rotation is perpendicular to the plane of incidence and reflection. What is the final angle of reflection of the light ray?
• A light ray strikes a plane mirror at an angle of $10^\circ$ to the normal. The mirror is rotated $30^\circ$ around the point where the beam strikes it, decreasing the angle of incidence. The axis of rotation is perpendicular to the plane of incidence and reflection. What is the final angle of reflection of the light ray?
• A light ray strikes a plane mirror at an angle of $40^\circ$ to the normal. The mirror is rotated $10^\circ$ around the point where the beam strikes it, increasing the angle of incidence. The axis of rotation is perpendicular to the plane of incidence and reflection. What is the final angle of reflection of the light ray?
• A light ray strikes a plane mirror at an angle of $50^\circ$ to the normal. The mirror is rotated $25^\circ$ around the point where the beam strikes it, decreasing the angle of incidence. The axis of rotation is perpendicular to the plane of incidence and reflection. What is the final angle of reflection of the light ray?

Objects and Plane-Mirror Images

• A plane mirror is a flat, smooth surface from which light is reflected by specular reflection.
• An object is a source of light rays that are to be reflected by a mirrored surface.
• Some of the light travels from the object to the mirror and reflects.
• Some of the reflected light from the object hits the observer's eyes.
• The brain processes this information as if the light has traveled in a straight line, giving the impression that the light came from a point behind the mirror.
• The combination of the image points produced by reflected light rays forms the image of the object.
• It is a virtual image, which is a type of image formed by diverging light rays.
• Images of real objects produced by plane mirrors are always virtual images.

Properties of Plane-Mirror Images

• Looking at yourself in a mirror, you also see that your image is oriented as you are, and it matches your size.
• You can draw rays from the object to the mirror to determine the size of the image.
• The sight lines of two rays originating from the bottom of an object will converge at the bottom of the image.

Plane-Mirror Image Height

• Using the law of reflection and congruent-triangle geometry, it can be shown that object height $(h<em>o)$ is equal to the image height $(h</em>i)$.
  • $h<em>o = h</em>i$

Plane-Mirror Image Position

• Looking at yourself in a mirror, you can see that your image appears to be the same distance behind the mirror as you are in front of the mirror.
• The position of the object with respect to the mirror $(x<em>o)$ has a length equal to the length of the apparent position of the image with respect to the mirror $(x</em>i)$.
  • $x<em>o = x</em>i$
• A plane mirror produces an image with the same orientation as the object.

Image Reversal

• There is a difference between you and the appearance of your image in a mirror.
• Left and right appear to be reversed by a plane mirror.
• It actually produces a front-to-back reversal.
• The mirror only reverses the object’s image such that it is facing in the opposite direction as the object.

Quiz

• Which is caused by a smooth surface, in which parallel light rays are reflected in parallel?
  • C. specular reflection (CORRECT)
• Which is caused by the scattering of light off a rough surface?
  • C. diffuse reflection (CORRECT)
• Which is a flat, smooth surface from which light is reflected by specular reflection?
  • C. plane mirror (CORRECT)
• Which is a type of image formed by diverging light rays?
  • D. virtual (CORRECT)
• Which is the correct relationship between object height, ho, and image height, hi, in a plane mirror?
  • A. ho = hi (CORRECT)