physicsrox chapter 5 light

╞╡§¥ Physics SPM 2015 Chapter 5: Light and Vision

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CHAPTER 5: LIGHT AND VISION

These notes have been compiled in a way to make it easier for revision. The topics are

not in order as per the syllabus.

5.1 Mirrors and Lenses

5.1.1 Image Characteristics

Image characteristics are described using the following three categories:

Size Same Image is exactly the same size as the object

Magnified Image appears bigger than the object

Diminished Image appears smaller than the object

Direction Upright Image appears to be in the same direction as the object

Inverted Image appears upside down compared to object

Type Real Real images are images you can capture on a screen.

Mirrors: Images are formed on the same side of the mirror as the object

Lenses: Images are formed on the opposite side of the lens from the object

Virtual Virtual images are images you can see but cannot capture on a screen.

Mirrors: Images are formed on the opposite side of the mirror from the object

Lenses: Images are formed on the same side of the lens as the object

5.1.2 Plane mirrors

Law of light reflection:

• The reflected angle is always the same as the incident angle.

• The incident ray, reflected ray, and normal line are in the same plane.

Characteristics of an image formed by a plane mirror:

Size Same

Direction Upright, laterally inverted

Type Virtual

Distance Distance of an image from the plane mirror is the same as the distance of the object from the

mirror

i r

normal Incident ray Reflected ray



5.1.3 Curved Mirrors vs Lenses

Concave mirror Convex mirror

Also known as Converging mirrors Diverging mirror

Focal lengths Positive

E.g. f = +20cm.

Negative

E.g. f = -20cm.

For both concave and convex mirrors, the focal length is half the radius; i.e. CF = FP.

Convex lens Concave lens

Also known as Converging lens Diverging lens

Focal lengths Positive

E.g. f = +20cm.

Negative

E.g. f = -20cm.

Determining the Position and Characteristics of an Image with a Ray Diagram

Concave mirror

A ray parallel to the principal axis

is reflected to pass through F

A ray through F is reflected

parallel to the principal axis

A ray through C is reflected back

along its own path

Convex mirror


is reflected as if it came from F

A ray towards F is reflected


A ray towards C is reflected back

along its own path



Convex lens


is refracted to pass through F

A ray through F is refracted


A ray through C travels straight

along its own path

Concave lens


is refracted as if it came from F

A ray towards F is refracted


A ray towards C travels straight

along its own path

To determine the position and characteristics of an image using a ray diagram:

1. Draw two rays emanating from the top of the object to the mirror or lens, and using the guide in the table above, draw their

reflected/refracted paths.

2. The image is produced at the intersection of the two reflected/refracted rays.



Images formed by a Concave Mirror / Convex Lens

Position of

object

Ray diagram of concave mirrors Ray diagram of convex

lenses

Characteristics of

image

Between F and

the mirror /

lens

Virtual

Upright

Magnified

At F

Virtual

Upright

Magnified

At infinity

Between F and

C/ 2F

Real

Inverted

Magnified

At C / 2F

Real

Inverted

Same size

Greater than C

/ 2F

Real

Inverted

Diminished

At infinity

Real

Inverted

Diminished

Images formed by a Convex Mirror / Concave lens

Position of

object

Ray diagram of convex mirror Ray diagram of concave lens Characteristics of

image

Anywhere in

front of the

mirror or

lens

Virtual

Upright

Diminished



SUMMARY OF COMPARISON OF IMAGE CHARACTERISTICS

Characteristics of concave mirrors are the same as convex lenses:

Object distance Image characteristics

u = ∞ Real Inverted Diminished

u > 2f Real Inverted Diminished

u = 2f Real Inverted Same Size

f < u < 2f Real Inverted Magnified

u = f Virtual Upright Magnified

u < f Virtual Upright Magnified

Characteristics of convex mirrors are the same as concave lenses:

Virtual, Upright, Diminished

Lens / Mirror

f 2f

Real, Inverted Virtual, Upright

Same size

Magnified Diminished



5.1.4 Lens Equation

fvu

111

where u = object distance [cm]

v = image distance [cm]

f = focal length of lens [cm]

5.1.5 Lens Power

fP

1

OR f

P100

where P = lens power [D]

f = focal length [m]

where P = lens power [D]

f = focal length [cm]

5.1.6 Linear Magnification

Linear magnification is the ratio of the image size to the object size.

u

v

h

hm

o

i

where m = linear magnification

hi = height of image

ho = height of object

5.1.7 Application of Lenses

Complex Microscope

Astronomical Telescope

Focal length, f

Convex lens: positive

Concave lens: negative

Object distance, u

Always positive

Image distance, v

If positive: real image

If negative: virtual image

fo < fe

|m| > 1: magnified

|m| = 1: same size

|m| < 1: diminished

If m is negative, take

the modulus value

fo > fe

Magnification =

e

o

f

f

Normal setting:

Length between lenses = fo + fe



5.2 Refraction and Total Internal Reflection

Light refraction is a phenomenon where the direction of light is changed when it crosses the boundary

between two materials of different optical densities. It occurs as a result of a change in the speed of light as

it passes from one medium to another.

When a light ray travels from medium A to

medium B which is optically denser than A

When a light ray travels from medium C to

medium D which is optically denser than C

The ray of light will refract towards normal; r < i The ray of light will refract away from normal; r > i

When a light ray crosses the boundary between two different mediums at a right angle

i = 0°, r = 0°

5.2.1 Snell’s Law

Snell’s Law states that the ratio of sin i to sin r is a constant.

r

i

sin

sin = constant

5.2.2 Refractive Index

The refractive index or index of refraction of a medium is equivalent to the optical density of a medium.

Note: A material with greater density may not necessarily have greater optical density.

The refractive index / index of refraction of a medium, n can be calculated as:

n =r

i

sin

sin

=

v

c

medium, in thelight of speed

air,in light of speed

=

d

D

depth,apparent

depth, actual

=

csin

1

(where c is the critical angle)



5.2.3 Total Internal Reflection

Critical angle, c is the value of the incident angle when the

refracted angle is 90°.

• When i is increased to be greater than c, the light will be

complete reflected back into the material. No light will be

refracted.

• This phenomenon is known as total internal reflection.

Conditions for total internal reflection:

1. Light must be traveling from an optically denser medium to a less dense medium.

2. The incident angle must be greater than the critical angle.

END OF CHAPTER

physicsrox chapter 5 light

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