Light and Optics - 4Propagation of light

Electromagnetic waves (light) in vacuum and matterReflection and refraction of lightHuygens’ principlePolarisation of light

Geometric opticsPlane and curved mirrorsThin lenses

InterferenceDouble slits

DiffractionSingle slitDouble slits

Luke Wilson (Luke.wilson@... Room E17)

2

Sign rules – these apply to all systems we will consider !

Object distanceObject on same side of a surface as the incoming light, the object distance s is positive.

Image distanceImage on the same side of a surface as the outgoing light, the image distance s’ is positive.

Curvature of spherical surfaceWhen the centre of curvature is on the same side as outgoing light, the radius of curvature is positive.

Image formation by a plane mirror

(a) (b)

In Fig (a), all rays that originate from P diverge from P’. Rays do not pass through P’, so image is virtualTriangles PVB and P’VB are congruent, so |s| = |s’|. Using our rules, s = -s’

In Fig (b), PVQ and P’Q’V are congruent, so y = y’. The lateral magnification is 1.

Spherical concave mirror – image of a point object

Centre of curvature, CVertex (centre of mirror surface) VCV is called the optic axis

P is object point on optic axis

s, s’ and R all positive

Consider α small, paraxial rays

All rays from P pass through P’ , real image

Let’s show this…

Spherical concave mirror – image of a point object

Exterior angle of triangle = sum of opposite interior angles

φβα

θαφθφβ

2

=+

+=+=

Eliminate θ

Now, assume small angle approx. tan x ≈ x

2'

11 2'

'

RssRh

sh

sh

Rh

sh

sh

=+⇒=+

=== φβα

Spherical concave mirror – focal point and focal plane

fssRf

RsRsRss

1'

11 2

2' 2

'11 2

'11

=+⇒=

=⇒=+∞

⇒=+

Spherical concave mirror – image of an extended object

Triangles VPQ and VP’Q’ are similar, so lateral magnification is

For m positive, image is erect. For m negative, image is inverted.

ss

yym ''

−==

Spherical convex mirror – image of a point object

2'

11 Rss

=+ss

yym ''

−==

… also apply here.

Note that s is positive, s’ is negative and R is negative

Spherical convex mirror – image of a point object

fss1

'11 =+ Still applies, f negative

Graphical methods for mirrors

1. Ray parallel to optic axis reflects through/ appears to come from focal point.

2. Ray through/ toward focal point reflects parallel to the axis.3. Ray through/ to centre of curvature intersects surface

normally, reflects along its original path.4. Ray to vertex reflects symmetrically around optic axis.

Graphical methods for mirrors

Note how image changes as object is moved closer to the mirror !

Example questionsA concave mirror has a radius of curvature of 22 cm. (a) Calculate the focal length. Does the focal length change if the mirror is submerged in water?

An object 0.5 cm tall is placed 16 cm to the left of the vertex of this mirror.(b) Determine the position, size, orientation of the image and whether it is real or virtual.

cm 112

+==Rf

cm 1.15.02.2'

2.216

2.35'

cm 2.3511161116'

11'

1 1'

11

=×==

−=−=−=

+=−×

=−

=⇒−

=

−==+

ymyssm

fssfs

sffs

sfsfss

So, image is real, inverted and larger

Spherical mirrors summary

Remember the sign rules !!!

Image-object relationship given by

Lateral magnification given by

fss1

'11 =+

ss

yym ''

−==