Mirrors (optics)

The importance of knowledge of lenses

Because they're employed all around us in devices like microscopes, binoculars and cameras, etc.

Without knowledge of these lenses, the working operation/principal of these devices can't be understood.

Mirror Writing

Leonardo da Vinci was an artist and scientist in the 15th century. He used ‘mirror writing’ in his notebooks when he was writing about his inventions and other ideas (human anatomy, war devices, etc.) Why do you think he did this?

Why do you think Leonardo wrote in reverse?

Several possibilities have been suggested:

• He was trying to make it harder for people to read his notes and steal his ideas. • He was hiding his scientific ideas from the powerful Roman Catholic Church, whose teachings sometimes disagreed with what Leonardo observed.

• He was trying to prevent smudging: writing left handed from left to right was messy, the ink just put down would smear as his hand moved across it.

Images in Plane Mirrors

You always wondered why the writings on the hood of a police car or ambulance appears backwards???

Virtual image: formed by light coming from apparent light source light not arriving at or coming from actual image location because no light rays are actually arriving at/coming from image location. It's produced with a diverging lens or convex mirror.

Can't be projected on screen
Must look at 3 optical device to see virtual image

When reflected light off plane mirrors enters eyes, brain project rays backwards to form apparent light souce located behind mirror.

Plane mirror divides object image line in half and is perpendicular to line

Image in plane mirror is always same size as object virtual (behind the mirror) upright and laterally inverted.

Vocabulary recap

Reflect: To bounce off.
Normal: Line drawn perpendicular to mirror's surface.

Characteristics of an image in Plane Mirror

Images undergo a lateral inversion - the orientation is backwards and in reverse order.

Lateral inversion means "apparent reversal of the mirror image's left and right when compared with the object" or simply means "sideways".

Lateral🪜Inversions examples

Images undergo a lateral inversion - the orientation is backwards and in reverse order.

Method to describe properties of an image

SALT

Size, Attitude, Location, Type

Size - Larger, Same Smaller
Attitude - Upright inverted
Location - Distance of image from mirrors of lens; in front of or behind mirror or lens
Type - Virtual, real

Summary of properties of an Image using S.A.L.T

Light rays and laws of reflection are used to explain how eye form image of light source behind opaque mirror.

Note: only light rays that are reflected off the mirror and into eyes contribute location of apparent source

Note: light rays behind mirror are draw as lines. Indicating the rays don't really exist. Your brain projects rays and virtual image behind mirror.

Recap on Mirrors

Curved Mirrors

To observe effect of light travelling in straight lines on formation of images
To observe a ‘real’ image
To apply laws of reflection for curved mirrors

Convex and Concave Mirrors

Convex mirrors face outward
Concave mirrors face inward

Avoid confusion for Convex & Concave

(Way to remember)

Concave is a "cave"

Note:
Concave's focal length is postivite and Convex's focal length is negative

Converging/Concave Mirrors

Concave's synonyms = converging, converge, dispersive, negative.

(however when it's a lens diverging is used instead of converging)

Unlike Convex mirrors which are positive, Concaves are negatives

Centre of Curvature (C or 2F): Centre of sphere whose surface is used to make mirror.

Principal Axis: Line through centre of curvature to midpoint of mirror.
Vertex (V): Point where principal axis meets mirror.

Focus (F): Point where reflected rays from parallel incident rays pass through/converge through/converge.

Concave's parallel rays fall on the mirror they converge/meet at a point called "focus"

That's why concave mirrors are sometimes called convert ging mirrors

Laws of Reflection in Converging (Concave) Mirrors

Light ray parallel to principal axis = pass through focus

Ray pass through focus = reflect parallel to principal axis

Ray pass through centre of curvature = reflected back itself

All ray parallalel to principal axis of convex mirror = will have extension pass that

Locating Image in Concave Mirror

Case A: Object is placed behind C

Case B: Object is placed at C

Case C: Object is placed between C and F

Case D: Object is placed at F

Case E: Object is placed in front of F

Real and Virtual Images

Formed when light rays converge at focal length after passing through or reflecting off optical device and

when light rays actually arrive at image location, when using converging lens or concave mirror.

Size of real image depends placement of object.
When object placed in front F, upright and virtual image is formed.

Erect: upright

Invert: upside down

Can be projected onto a screen and is formed by actual convergence of light rays.
When object placed beyond F, inverted and real image is formed.

Properties of images in Concave Mirrors

Properties of images in Convex Mirrors

When Object=C = forms Z shape line

Object larger and bigger when approaching
When Object=F = no image, attitude is clear
When Object<F magnified

Applications of Converging Mirrors

Searchlights
Satellite dishes
Solar cookers

Concave mirrors cause reflected rays to converge to a central point (Focus), giving a bright, forward, beam of light. The less curvature, longer the focal length.

Diverging/Convex mirror

Ray diagrams of formation of image by convex lens

Unlike Concave mirrors which are negatives, Concex are positives

Optical Center

Center of Curvature

Convex lens have 2 spherical faces. Each forms part of sphere.

Centers of spheres called "Center of Curvature" of lens. Since there are 2 center. We represent as C1 and C2 👇

Principal Axis

As mentioned, principal axis is imaginary line passing 2 centers of curvatures C1 and C2 of lens.

Aperture

Principal focus of convex lens

Focal length

Position of F1, F2, 2F1 and 2F2 on principal axis

Rule 1#

Rule 2#

Rule 3#

Convex mirrors cause reflected rays to diverge, giving a much wider field of view.

In a convex/diverging mirror, F and C are behind the reflective surface.

A ray aimed at the focus is reflected parallel to the principal axis.
A ray aimed at the centre of curvature is reflected back on itself.

* Images will always be smaller and virtual because rays never cross to form real image.

Ray diagrams (Convex mirror)

Blue thing is object with its ray go through mirror.

2. The line will then leave the mirror as if it had come from the focus.

3. Second line travels directly to Center of curvature (C) will reflect back along same line.

We always need to draw arrow's head going both way

4. We can see that crossed part is where object is. As we can object is also smaller

Description of image:

S: smaller

A: upright

L: between F&V

T: virtual

Image in convex mirror = true

Uses of convex/diverging mirrors

Rear-view mirrors

Security mirrors

Ray diagrams (Concave mirror)

Draw from tip of object (green arrow) parallel to principal axis to mirror.
Blue line then go to focus point (f)

Example 1#

3. A next line will go from tip of object to focus point

4. Second line go to bounce from mirror to left side paralling the axis.

Left bottom part where lines intersect is where image appears (always somewhere between C and 2f and always smaller than object)

When object greater than C away --> always inverted and real.

In this example when the object distance (do) always = C,

image distance (di) always = C and same size as object

Example 2#

In this one, when the object is between C and f its image is always greater than C, still a real image and inverted.

Example 3#

This one, first line again drawn from tip to mirror bouncing back to f.

But for second line since object is on f, the line is from tip to mirror and bounce back and paralling first line. Resulting no image.

Example 4#

Last example being object in front of f. As usual first line go from tip to mirror bouncing back to f.

But second line will go the axis and has to bounce back to form same angle on both side of line between axis.

Second line never parallel the first one in these situations making them diverging rays, (don't meet at a point and lines goes away).

Image now bigger and behind mirror, as it's upright (also called "erect"). It's now also virtual image being image created by diverging light rays that eyes follows behind mirror.

Example 5#

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