• The image formed by a pinhole camera can be explained if we know that light travels in straight lines.
• The smaller the pinhole the sharper (more focussed) the image.
• The smaller the pinhole the dimmer the image for the same exposure time.

Almost all of the time light travels in straight lines. This can easily be proven because of the existence of shadows. If light were able to bend around corners, then there would be no shadow. The light from the sun, a light source, etc. all travel in straight lines unless one of three things happens to bend the light ray.

a) Reflection - light bounces off an object.

b) Refraction - light bends as it passes into another substance (or medium)

c) Diffraction - light bends as it passes near an object or through a small opening

In the following diagram as with all situations involving reflection. The angle of incidence (i) equals the angle of reflection (r). i.e. i° = r°

There are two ways that an image can be found in a plane mirror

a) Ray Tracing

The light rays that enter the eye are traced back to a point where they converge, this point is known as the image. This can be seen in the following diagrams.

Now we trace the rays going to the eye straight back.

The point where these rays meet is called the image.

There are two observations we can make about the object and the image.

1. The line joining them is perpendicular to the plane of the mirror.

2. They are the same distance form the surface of the mirror.

Example.

A person 1.8m tall stands in front of a mirror. How big is the mirror if he wants to see all of his image and is a distance i) 3m ii) 6m iii) 10m from the mirror. (Do the first get students to do the next two)

b) Parallax Method

Line up a pin with the image in the mirror. This is simply done by moving a pin around behind the mirror until the pin's position coincides with that of the image.

When an image is formed there are a number of things that can be said about it. It may be:

Real - able to be projected onto a screen

or Virtual - unable to be projected onto a screen.

AND Erect - standing the same way up as thee object

or Inverted - standing the opposite way up to the object.

AND Enlarged - bigger than the object

or Diminished - smaller than the object

or The same size.

Diffuse reflection is the sort of reflection that allows us to see the objects around us. It occurs when light is reflected from a rough surface, such as a picture screen.

The angle of incidence (i) equals the angle of reflection (r), but because of the rough surface the light is reflected in a large range of directions.

Here we use the ray tracing method to find where an image is formed. As usual i° = r° , but through experiments it has been found that the rays of light parallel to the principal axis all converge on a single point, called the focus.

The distance from the focus to the mirror is known as the focal length. Light rays follow the same path no matter what end they are shone from. ( This is the principle of reversibility of light.) A light ray going through the focus will be reflected parallel to the principal axis.

Thus we have two rays we can trace, and an image will be formed where the two rays meet.

Distant objects produce images close to the focus. The more distant the object the closer to the focus an image will be formed. Thus if an object is positioned at infinity it will have an image located at the focus.

Magnification of an image is defined as

When the object is at a distance equal to twice the focal length, then the image is formed at the same place, is inverted and the same size as the object. This is the only time at which the image is the same size as the object. This point on the axis is called the centre of curvature (C). The distance from this point to the mirror is called the radius of curvature (r) and r = 2f.

Example

1. Find the image using a ray diagram and state it's nature, for an object 5cm high in front of a concave mirror of focal length 20 cm at a distance of a) 40 cm b) 30 cm c) 20 cm d) 10 cm (Do the 1st set the rest)

2. An object 4 cm high is placed in front of a concave mirror of focal length 10 cm at a distance of 50 cm. Find the image and state it's nature.

Another sort of mirror is the convex or diverging mirror. Because of the shape of this mirror any light striking the mirror will be diverged, thus making it impossible to form a real image. Consider rays of light parallel to the principal axis. These light rays are diverged by the mirror as if they had come from a focus behind the mirror, known as a virtual focus.

As for the concave mirror we would expect a ray of light travelling towards the virtual focus to be reflected parallel to the principal axis.

With a convex mirror we find that the image is always virtual, erect, diminished, behind the mirror and located between the mirror and the focus.

Example

An object 4 cm tall in front of a convex mirror with a focal length of 10 cm at a distance from the mirror of a) 40 cm b) 20 cm c) 5 cm. Find the position of the image in each case. (do the first set the rest)

Refraction occurs when light rays travelling from one substance to another bend.

In all cases of refraction we have part of the incident ray being reflected.

We can shine light from one substance (a) to another substance (b), and we find for pairs of angles (incidence and refraction) that the ratio sin i° ¸ sin r° = a constant. This constant is called the refractive index (n_a,b).

so

This formula is known as Snell's law.

In the case where light travels from one substance to another the refractive index is called the relative refractive index or relative indexes of refraction. i.e. n_a,b is the refractive index of b relative to a. eg. n_air,glass = 1.50000

There is also a quantity known as the absolute index of refraction. This is the index of refraction for light passing from a vacuum to a substance, and only one subscript is used. eg. n_glass is the absolute index of refraction for glass. n_glass = 1.50044

Consider the case of light entering into and exiting from a parallel sided block.

At boundary 1 Snell's law says

At boundary 2 Snell's law says

but

Thus

Consider the situation where light travels from substance 1 into substance 2, with a vacuum between them.

At boundary 1

At boundary 2

Thus Equation 1

But if there was no vacuum between the substances we would have

and Snell's Law says Equation 1

equation 1 can be rearranged to get

Thus

Example n_air =1 n_glass = 1.5 q _g = 20° , 40° . Find q _a

Light travelling from a high refractive index to a low refractive index bends away from the normal.

Light travelling from a low refractive index to a high refractive index bends towards the normal.

In the situation where the light ray bends away from the normal there is a time when the angle of refraction is 90° .

There after the light cannot be refracted into the second substance, and must be reflected back into the first substance. In this situation the product n_1,2 sin q ₂ is > 1 and no value of sin q ₁ is possible. This phenomenon is called Total Internal Reflection. The angle of incidence producing an angle of refraction of 90° is called the critical angle (q _c).

Let us now find an equation involving the critical angle.

We know q ₁ = q _c and q ₂ = 90°

using the equation

we get

since sin 90 = 1

Note: sin q _c £ 1, n₂ £ n₁ for T.I.R.

Example

Light travelling from glass to air. n_air = 1.0, n_glass = 1.5, i = 45° . Find q c

This phenomenon is the breaking up of white light into it's component colors. This is best observed in a prism.

The violet light is bent more than the red light. This means that the different colors have different angles of refraction for the same angle of incidence. i.e. Violet light has a larger refractive index for a given substance than does red light.

Rime: Violet Varies Violently

Colors: R O Y G B I V

1. For the following pairs of refractive index find q c

Diamond - Air n_d = 2.4 n_a = 1.0

Glass - Water n_g = 1.5 n_w = 1.33

Diamond - Water n_d = 2.4 n_w = 1.33

Diamond - Ether n_d = 2.4 n_e = 1.36

2. A fish is at a depth of 20 cm in a tank of water. Calculate the area of the circle through which the fish can see. n_w = 1.33, n_a = 1.00

Text Page 89 Questions 25 - 36

When light shines on a colored object the dye particles absorb some of the colors and the remaining color is reflected into our eyes.

Black objects absorb all of the colors and do not reflect any light, so appear black.

White objects reflect all the colors, so appear white.

The behaviour of light through a lens is such that the light rays are refracted at each surface of the lens.

As an object is move further away from a lens then the angle inside the cone of light reaching the lens becomes smaller.

If we went to a very distant light source (such as the Sun) then the light rays would effectively be parallel.

In a convex lens the parallel light is bent so that it converges on a point where it forms an image. This special point is called the principal focus of the lens. A concave lens would diverge the light as though it came from a point. A lens has two focal points one on each side of the lens and equal distances from the lens. This distance is called the focal length.

There are three light rays which are easy to follow, they are:

1. Rays travelling parallel to the principal axis are:

Ray diagrams should always be done accurately, to scale and include a scale with the diagram.

Object outside the focal length.

The image is real, inverted, may be diminished or enlarged and the opposite side to the object.

Object inside the focal length.

The image is erect, enlarged virtual and the same side as the object.

The image is always virtual, diminished, erect and between the lens and the focus.