Reflection of light Revision Notes

When a light ray strikes a reflective surface, the point where it meets the surface is called the point of incidence.

The normal is an imaginary line drawn perpendicular (at 90°) to the surface at the point of incidence.

This line serves as a reference to measure angles related to the incoming and reflected rays.

• The normal is always perpendicular to the surface at the point of incidence.
• It is an imaginary line used for angle measurement, not a physical object.

The angle of incidence (denoted as i) is the angle between the incident ray (incoming light ray) and the normal.

It is measured in degrees (°) and always taken from the normal to the incident ray, not from the surface.

This angle quantifies how the incoming light approaches the surface.

• Angle of incidence is measured between the incident ray and the normal.
• Units are degrees (°).
• It is always measured from the normal, never from the surface.

The angle of reflection (denoted as r) is the angle between the reflected ray (light ray leaving the surface) and the normal.

Like the angle of incidence, it is measured in degrees from the normal to the reflected ray.

This angle describes the direction in which light is reflected from the surface.

• Angle of reflection is measured between the reflected ray and the normal.
• Units are degrees (°).
• It is always measured from the normal, not the surface.

The law of reflection states that the angle of incidence is equal to the angle of reflection: i = r.

This law applies to all smooth reflective surfaces, such as plane mirrors.

It means that light reflects symmetrically about the normal line.

• Angle of incidence equals angle of reflection (i = r).
• This is a fundamental law in optics.
• It applies to plane mirrors and other smooth reflective surfaces.

To draw a ray diagram for reflection: first draw the reflective surface as a straight line.

At the point where the incident ray meets the surface, draw the normal line perpendicular to the surface.

Draw the incident ray approaching the surface, making an angle i with the normal line (measured with a protractor). Then draw the reflected ray leaving the surface, making the same angle r = i with the normal on the opposite side of the normal line from the incident ray.

• Draw the surface as a straight line.
• At the point of incidence, draw the normal perpendicular to the surface.
• Measure and draw the incident ray at angle i to the normal.
• Draw the reflected ray at angle r equal to i on the opposite side of the normal.
• Label all angles and rays clearly.

A plane mirror is a flat, smooth reflective surface that obeys the law of reflection: the angle of incidence equals the angle of reflection. When light rays from an object strike the mirror, they reflect according to this law. The reflected rays appear to come from a point behind the mirror, forming an image.

The image formed by a plane mirror is called an optical image because it is formed by the reflection of light rays. This image is not a physical object but a perception created by the brain interpreting the reflected rays.

Images formed by plane mirrors have specific, consistent features:

1. Size: The image is the same size as the object. This means the height and width of the image match those of the object exactly.

2. Position: The image appears to be located the same distance behind the mirror as the object is in front of it. This distance is measured along a line perpendicular to the mirror surface, called the normal line. The image is laterally inverted (left and right are reversed). 3. Nature: The image is virtual, meaning it cannot be projected onto a screen because the light rays do not actually converge at the image location; they only appear to do so when extended backwards.

To illustrate image formation, a ray diagram can be drawn following these steps:

1. Draw a straight line to represent the plane mirror. Mark the mirror surface with a vertical line.

2. Place the object in front of the mirror, represented by an arrow perpendicular to the mirror surface (the object arrow). The base of the arrow lies on the mirror’s normal line (perpendicular to the mirror). 3. Draw at least two incident rays from the top of the object arrow towards the mirror: one ray perpendicular (normal) to the mirror, which reflects back on itself, and another ray at an angle to the mirror surface. 4. Apply the law of reflection: the angle of incidence equals the angle of reflection for each ray. Draw the reflected rays accordingly. 5. Extend the reflected rays backward behind the mirror using dashed lines. The point where these backward extensions intersect locates the top of the image arrow. 6. Draw the image arrow behind the mirror, the same size as the object arrow, at the same distance from the mirror as the object.

A virtual image is one where the light rays do not actually meet but only appear to diverge from a point behind the mirror. Because the rays do not physically converge, the image cannot be projected onto a screen placed behind the mirror.

In plane mirrors, the virtual image is always upright and the same size as the object. This contrasts with real images, where rays converge and can be projected onto a screen.

The brain interprets the reflected rays as if they come from behind the mirror, creating the perception of the image.

The key properties of images formed by plane mirrors can be summarised as follows:

Size: Image size equals object size (magnification = 1).

Distance: Image distance behind mirror equals object distance in front (image distance = object distance). - Nature: Image is virtual and upright, cannot be projected onto a screen. - Orientation: Image is laterally inverted (left-right reversed).

When a ray of light strikes a reflective surface, it changes direction by bouncing off the surface. To describe this process, we use the following terms:

The **normal** is an imaginary line perpendicular (at 90°) to the surface at the point where the light ray meets the surface.

The **angle of incidence (i)** is the angle between the incoming ray (incident ray) and the normal line at the point of incidence, measured in degrees (°). It is always measured from the normal, not the surface itself, to ensure consistency in angle measurement. The unit is degrees (°). For example, if the incident ray makes a 30° angle with the normal, then i = 30°.

• Normal: perpendicular line to surface at point of incidence.
• Angle of incidence (i): angle between incident ray and normal, measured in degrees.

The **law of reflection** states that the angle of incidence is always equal to the angle of reflection. This means:

\[ \boxed{\text{angle of incidence} = \text{angle of reflection}} \quad \text{or} \quad i = r \]

where: i = angle of incidence, r = angle of reflection, both measured from the normal in degrees (°). This law applies to all reflective surfaces, including plane mirrors and smooth shiny surfaces. The reflected ray is the ray that leaves the surface after reflection, making an angle r with the normal.

• Angle of incidence equals angle of reflection (i = r).

Reflection occurs because light behaves as a wave that interacts with the surface atoms. When the light wavefront hits a smooth surface, the electrons in the surface atoms oscillate and re-emit the light wave. The direction of the reflected wavefront is such that the angle of incidence equals the angle of reflection. This is a consequence of the wave nature of light and the boundary conditions at the surface.

If the surface is rough, the reflected rays scatter in many directions, causing diffuse reflection. The law of reflection still holds locally at each point, but the overall reflection is scattered.

• Reflection is due to light waves interacting with surface atoms.

To draw a ray diagram illustrating reflection from a plane mirror:

1. Draw a straight line to represent the mirror surface.

2. At the point where the incident ray meets the mirror, draw the normal line perpendicular to the mirror surface (90°). This is usually a dashed line for clarity but must be clearly marked as the normal line at the point of incidence. 3. Draw the incident ray approaching the mirror, making an angle i with the normal. 4. Using a protractor, measure the same angle on the opposite side of the normal to draw the reflected ray, ensuring the angle of reflection r equals i. 5. Label the angles i and r clearly, and mark the incident ray, reflected ray, normal, and mirror surface. 6. The reflected ray should be on the same side of the normal as the mirror surface but leaving away from the point of incidence.

• Draw mirror and normal at point of incidence.
• Measure angle of incidence from normal.

The law of reflection can be used to solve problems involving the direction of reflected rays. For example, if a ray strikes a mirror at 40° to the normal, the reflected ray also makes 40° with the normal but on the opposite side.

This principle is essential in designing optical devices such as periscopes, kaleidoscopes, and in understanding how images form in plane mirrors.

When multiple reflections occur (e.g., in corner reflectors), the law applies at each reflection point independently.

• Use i = r to find direction of reflected rays.

Reflection occurs when light rays strike a surface and bounce off. For plane mirrors, which have a flat reflective surface, the reflection follows a precise rule called the law of reflection.

The law of reflection states: The angle of incidence (i) is equal to the angle of reflection (r). Both angles are measured with respect to the normal, an imaginary line perpendicular to the mirror surface at the point of incidence.

This law is fundamental in predicting the path of reflected rays and understanding image formation in plane mirrors. The image formed is virtual (cannot be projected on a screen), upright, laterally inverted, and the same size as the object. The image distance behind the mirror equals the object distance in front of it.

• Angle of incidence (i): angle between incident ray and normal.
• Angle of reflection (r): angle between reflected ray and normal.
• Law of reflection: i = r.

To represent reflection accurately, a ray diagram is drawn using a ruler and protractor. The steps are:

1. Draw a straight horizontal line to represent the plane mirror.

2. Mark the point of incidence where the incident ray strikes the mirror surface; label it point O. Draw the normal at O as a dashed line perpendicular to the mirror surface (90° to the mirror). Use a protractor to ensure accuracy. The normal is not part of the mirror but a reference line for measuring angles. 3. Draw the incident ray approaching point O at a chosen angle to the normal. Measure and label the angle of incidence (i) between the incident ray and the normal. 4. Using the law of reflection, draw the reflected ray leaving point O such that the angle between the reflected ray and the normal equals the angle of incidence. Label this angle of reflection (r). 5. Extend the reflected ray backward behind the mirror with a dotted line to locate the virtual image position if required.

• Use a ruler for straight lines and a protractor for angle measurement.
• Label all rays and angles clearly.

To measure angles accurately: Place the protractor so that its centre hole is exactly at the point of incidence on the mirror line. Align the baseline of the protractor with the mirror surface. Measure the angle between the incident ray and the normal line; this is the angle of incidence (i). Similarly, measure the angle between the reflected ray and the normal; this is the angle of reflection (r). Repeat measurements several times to improve accuracy and calculate an average. Record all measurements with units in degrees (°).

• Use a sharp pencil for precise lines.
• Ensure the protractor is correctly aligned to avoid parallax errors.

The primary calculation involves verifying the law of reflection: i = r. If one angle is unknown, it can be calculated by rearranging the equality.

Example formula: \[ r = i \quad \text{or} \quad i = r \]

If the angle of incidence is given, the angle of reflection is equal to it, and vice versa. No other complex calculations are required for plane mirror reflection at this level.

• Use the law of reflection to find unknown angles.

A light ray strikes a plane mirror at an angle of incidence of 35°. Calculate the angle of reflection.

Step 1: Write down the law of reflection: \[ i = r \]

Step 2: Substitute the known value: \[ r = 35° \] The angle of reflection is 35° (to the normal). Step 3: State the answer with units: The angle of reflection is 35°. Common error: Confusing the angle with respect to the mirror surface instead of the normal. Always measure angles from the normal, not the mirror surface.

• Formula: i = r
• Substitution: r = 35°