35. Mirrors and images

Huygens’s Principle (analysis of wave propagation):

From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave.

Huygens’s Principle (analysis of wave propagation):

From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave.

Can be used to derive

Snel’s law and more

generally the properties

of mirrors and lenses

Huygens’s Principle (analysis of wave propagation):

From the work of Christian Huygens in 1678, the geometrical analysis reveals that every point of a wave front can be considered to be a source of secondary wavelets that spread with a speed equal to the speed of propagation of the wave.

Examples: Fata Morgana (mirage)

Source: dailymail

Examples: Fata Morgana (mirage)

cold

hot

(hot air has lower index of refraction)

Source: dailymail

Examples: Fata Morgana (mirage)

Source: dailymail

es.wikipedia.org

Where is the image reflected in a typical mirror?

A. Mainly from the glass

B. Mainly from the metal behind the glass

C. Mainly from the back side of the glass covered by

black color

Reflection from a mirror

Plane Mirrors

Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if they

pass from a material of one index to another.

Direct images:

In air

Plane Mirrors

Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if the

pass from a material of one index to another.

Direct images:

In air

From inside material

Plane Mirrors

Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if the

pass from a material of one index to another.

Direct images:

In air

From inside material Mirror image:

Plane Mirrors

Constructing the image: Following the light rays to form an

image of an object.

Virtual image

Plane Mirrors

Constructing the image: Following the light rays to form an

image of an object.

Virtual image

Negative distance

What is the magnification of the mirror image (flat mirror)?

A. -1

B. 1

C. 0

D. Other

Plane Mirrors

Constructing the image: Following the light rays to form an

image of an object.

Negative distance

Magnification:

𝑚 =𝑦′

𝑦= −

𝑠′

𝑠

Object y: Image y’:

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓= 0 ⇒ 𝑠 = −𝑠′

f (the focal point) = infinity

Two important relations for mirrors:

Two concepts:

real and virtual

images

Plane Mirrors

Constructing the image: Following the light rays to form an

image of an object.

Which one is the real object?

A. Top one

B. Bottom one

C. None

Xinhua News Agency

Measuring 500 meters in

diameter, the radio telescope is

nestled in a natural basin within a

stunning landscape of lush green

karst formations in southern

Guizhou province. It took five years

and $180 million to complete

The telescope requires a radio

silence within a 5-kilometer (3-mile)

radius, resulting in the relocation of

more than 8,000 people from their

homes in eight villages to make

way for the facility.

Spherical Mirrors

The focal point is at half of the mirror’s radius of curvature. The focal length is the distance from the vertex to the focal point.

All incoming rays will converge at the focal point.

Spherical Mirrors

vertex

Spherical concave mirror

http://www.fas.harvard.edu

Image examples:

Possible images

Spherical Mirrors

Image properties:

Object

Image

Magnification:

𝑚 =𝑦′

𝑦= −

𝑠′

𝑠

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓

Concave mirror

Spherical Mirrors

I have a concave spherical mirror of radius 2m, I place an object at 4m from the mirror, what is

the magnification of the object?

A. M=1/3

B. M=-1/3

C. M=1

D. M=-1

E. M=3

F. M=-3

Image examples:

Object far away from mirror

Object

Image

Magnification:

𝑚 =𝐼𝑚𝑎𝑔𝑒

𝑂𝑏𝑗𝑒𝑐𝑡= −

𝑠′

𝑠Object-image relationship:

1

𝑠+1

𝑠′=1

𝑓

𝑠s’

Spherical Mirrors

Image examples:

Object far away from mirror

Object

Image

Magnification:

𝑚 =𝐼𝑚𝑎𝑔𝑒

𝑂𝑏𝑗𝑒𝑐𝑡= −

𝑠′

𝑠=

𝑓

𝑓 − 𝑠< 0

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓

𝑠s’

Spherical Mirrors

Image examples:

Object far away from mirror

Object

Image

Magnification:

𝑚 =𝐼𝑚𝑎𝑔𝑒

𝑂𝑏𝑗𝑒𝑐𝑡= −

𝑠′

𝑠=

𝑓

𝑓 − 𝑠< 0

and |m|<1

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓𝑠

s’

Spherical Mirrors

I have a concave spherical mirror of radius 4m, I place an object at 1m from the mirror, what is

the magnification of the object?

A. M=1/2

B. M=-1/2

C. M=1

D. M=-1

E. M=2

F. M=-2

Image examples:

Object close to mirror

ObjectImage

Magnification:

𝑚 =𝐼𝑚𝑎𝑔𝑒

𝑂𝑏𝑗𝑒𝑐𝑡= −

𝑠′

𝑠=

𝑓

𝑓 − 𝑠> 1

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓

Spherical Mirrors

s s’

Image examples:

Object close to mirror

ObjectImage

Magnification:

𝑚 =𝐼𝑚𝑎𝑔𝑒

𝑂𝑏𝑗𝑒𝑐𝑡= −

𝑠′

𝑠=

𝑓

𝑓 − 𝑠> 1

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓

Spherical Mirrors

s s’

For example:

R=4=>f=2; s=1; 1+1/s’=1/2=>s’=-2; m=2

Position of object Position of image Nature of image

dO < F Behind the mirror Virtual, enlarged, upright

dO = F No image No image, rays reflected parallel

F < dO < C Beyond C Real, enlarged, inverted

dO = 2F At C Real, same size, inverted

dO > 2F Between F and C Real, reduced, inverted.

dO = ∞ At F of size zero

Image examples:

All possibilities with

Concave mirror of radius C

physics.tutorvista.com

Spherical Mirrors

Double lens trick

dev.physicslab.org

Spherical Mirrors

Convex mirror

Spherical Mirrors

Convex mirror (negative focal length):

Magnification:

𝑚 =𝑦′

𝑦= −

𝑠′

𝑠

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓

f<0

(s>0 and s’<0 –> virtual image)

Spherical Mirrors

Convex mirror (negative focal length):

Magnification:

𝑚 =𝑦′

𝑦= −

𝑠′

𝑠

Object-image relationship:1

𝑠+1

𝑠′=1

𝑓

f<0

(s>0 and s’<0 => image is opposite to outgoing ray