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5.1.6 Images Formed by Curve Mirror

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Finding the Position and Size of the Image

  1. Any two rays are sufficient to fix the position and size of the image. Look for the point where the rays cross after reflection from the mirror.
  2. The interception of the two rays is the focus of the ray.
Example

The Ray Diagram and the Types of Image

The nature and size of the image formed by concave mirrors depends on the distance of the object from the mirror. This will be explained in the following sections.

 

5.1.4 Reflection of Light by Curved Mirror

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Curved Mirror

  1. A curve is part of a circle. Therefore
    1. the centre of the circle will also be the centre of the curve and is called the centre of curvature, and
    2. the radius of the circle will be equal to the radius of the curve, called the curvature radius.

Important Terms


All rays parallel to the principle axis will focus at F


Centre of curvature, C The geometric centre of a hollow sphere of which the concave or convex mirror is a part.
Pole of mirror, P The centre point on the curved mirror.
Principal axis A line which passes through the centre of curvature, C and the pole of a curved mirror, P.
Radius of curvature, r Distance between the pole, P and the centre of curvature, C.
Principal focus, F A point through which all rays travelling parallel to the principal axis converge to or appear to diverge from after reflection by the mirror.
Focal length, f The distance between the principal focus, F and the pole of the
curved mirror, P.
Aperture of mirror The portion of the surface of the mirror that reflects light.
Object distance, u Distance of object from the pole of the mirror, P.
Image distance, v Distance of image from the pole of the mirror,

 

5.1.3 Constructing Ray Diagram for Plane Mirror

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Steps to draw a ray diagram for an image in a plane mirror 

Step 1



( Draw the virtual image. Distance of object = Distance of image )

Step 2


( Draw 2 reflected rays, one from the image to the top of the eye and the other one from the image from the bottom of the eye. )

Step 3

( Draw the respective incident rays for the reflected rays you draw in step 2. )

 

 

5.1.2 Images Formed by Plane Mirror

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Plane Mirror

Images in plane mirrors

(Reflection of light on a plane mirror)
  1. Figure to the right shows how, by reflecting light, a plane mirror forms an image of a point source of light such as a small light bulb.
  2. The image forms in a mirror is
    1. Upright
    2. Virtual
    3. Laterally inverted
    4. Same size as the object

 

5.1.1 Reflection of Light

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Note: Both the angle of incident and angle of reflection must be measured from the normal.

Laws of Reflection

  1. The law of reflection state that
    1. The angle of incidence is equal to the angle of reflection; the ray leaves the surface at the same angle as it arrives.
    2. The incident ray, the reflected ray and the normal all lie in the same plane; all three could be drawn on the same flat piece of paper

Type of Mirror


 

4.4.4 Pressure Law

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Pressure law states that for a fixed mass of gas, the pressure of the gas is directly proportional to the absolute temperature of the gas provided the volume of the gas is kept constant.


Formula:


Explanation

  1. The kinetic energy of gas molecules increases with temperature.
  2. The air molecules collide with the wall of the container at higher velocity and frequency.
  3. The pressure in the gas increases, causing an increase in volume.

Graph

  1. In the graphs above, the first graph shows that P is directly proportional to the absolute temperature.
  2. The second graph shows that, if the temperature is in °C, the graph does not pass through the origin.
  3. The third and the forth graphs shows that P/T is always constant for all value of P and T.


Example 2:
An iron cylinder containing gas with pressure 200kPa when it is kept is a room of temperature 27°C. What is the pressure of the gas when the cylinder is located outdoor where the temperature is 35°C.

Answer:
P1 = 200kPa
T1 = 273 + 27 = 300K
P2 = ?
T2 = 273 + 35 = 308K

 

4.4.3 Charles’ Law

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Charles’ law states that for a fixed mass of gas, the volume of the gas is directly proportional to the absolute temperature of the gas provided the pressure of the gas is kept constant.


Formula:

Explanation

  1. When temperature increases, the average kinetic energy of the gas particles will increase.
  2. The air molecule move faster and collide with the wall of the container more vigorously at higher frequency.
  3. As a result, the space between the gas particles increases and the volume of the gas increases.

Graph

  1. In the graphs above, the first graph shows that V is directly proportional to the absolute temperature.
  2. The second graph shows that, if the temperature is in oC, the graph does not pass through the origin.
  3. The third and the forth graphs shows that V/T is always constant for all value of V and T.
Example 3:


The figure shows some air trapped in a capillary tube. Given that the temperature of the air is 27°C. Find the length of the air column when the temperature of the air is increased to 87°C.

Answer:
V1 = 6cm
T1 = 273 + 27 = 300K
V2 = ?
T2 = 273 + 87 = 360K

 

4.4.2 Boyle’s law

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Boyle's law states that the pressure of a gas with constant mass is inversely proportional to its volume provided the temperature of the gas is kept constant.


Formula:

Explanation 

  1. When the volume of gas decreases, the number of gas particles per unit volume increases.
  2. As a result, the frequency of collision between the air particles and the wall of the container increases.
  3. As such, the pressure of the gas increases.

Graph

  1. In the graphs above, the first graph shows that P is inversely proportional to V. 
  2. The second graph shows that P is directly proportional to 1/V. 
  3. The third and the forth graphs shows that PV is always constant for all value of V and P.

Example 1:
A fish releases a bubble of air of volume 1cm³ at the bottom of a lake. The depth of the lake is 10m. Find the volume of the bubble when it reaches the surface of the pond. (Assume that the atmospheric pressure is equal to 10m of water)

Answer:
V1 = 1cm³
P1 = 20m water
V2 = ?
P2 = 10m water


 

4.4.1 Pressure, Temperature and Volume of Gas

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The kinetic theory of gases explains the the relationship between the pressure, temperature and volume of gases base on the following assumptions:

  1. The gas consists of very small particles, each of which has a mass.
  2. These particles are in constant, random motion.
  3. The rapidly moving particles constantly collide with each other and with the walls of the container. All these collisions are perfectly elastic.
  4. There are forces of attraction between particles of matter. These attraction forces will increase as the distance between the particles becomes closer.
  5. The average kinetic energy of the gas particles depends only on the temperature of the system. The higher the temperature, the higher the kinetic energy of the particles.