Light and Optics - 4 - Sheffield
Transcript of Light and Optics - 4 - Sheffield
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 ''
−==