physics 121: optics, electricity & magnetism · neil alberding (sfu physics) physics 121:...
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![Page 1: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/1.jpg)
Moonbows
Friday somebody asked if rainbows can be seen at night.
It’s true...
...but they’re called Moonbows
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 25
![Page 2: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/2.jpg)
Moonbows
Friday somebody asked if rainbows can be seen at night.
It’s true...
...but they’re called Moonbows
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 25
![Page 3: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/3.jpg)
Moonbows
Friday somebody asked if rainbows can be seen at night.
It’s true...
...but they’re called Moonbows
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 25
![Page 4: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/4.jpg)
Moonbows
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 25
![Page 5: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/5.jpg)
Moonbows
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 3 / 25
![Page 6: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/6.jpg)
Diverging Lenses
For diverging lenses we draw the same three sets of rays
Parallel rays will appear to come from the near focal point
Rays directed toward the far focal point will come out parallel
Rays directed at the center of the lens will be unbent
A virtual image is formed on the object-side of the lens (s� is
negative)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 4 / 25
![Page 7: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/7.jpg)
Diverging Lenses
For diverging lenses we draw the same three sets of rays
Parallel rays will appear to come from the near focal point
Rays directed toward the far focal point will come out parallel
Rays directed at the center of the lens will be unbent
A virtual image is formed on the object-side of the lens (s� is
negative)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 4 / 25
![Page 8: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/8.jpg)
Diverging Lenses
For diverging lenses we draw the same three sets of rays
Parallel rays will appear to come from the near focal point
Rays directed toward the far focal point will come out parallel
Rays directed at the center of the lens will be unbent
A virtual image is formed on the object-side of the lens (s� is
negative)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 4 / 25
![Page 9: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/9.jpg)
Diverging Lenses
For diverging lenses we draw the same three sets of rays
Parallel rays will appear to come from the near focal point
Rays directed toward the far focal point will come out parallel
Rays directed at the center of the lens will be unbent
A virtual image is formed on the object-side of the lens (s� is
negative)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 4 / 25
![Page 10: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/10.jpg)
Diverging Lenses
For diverging lenses we draw the same three sets of rays
Parallel rays will appear to come from the near focal point
Rays directed toward the far focal point will come out parallel
Rays directed at the center of the lens will be unbent
A virtual image is formed on the object-side of the lens (s� is
negative)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 4 / 25
![Page 11: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/11.jpg)
Thin Lenses: Refraction Theory (23.7)
The figure above shows a spherical boundary between two media
with indices of refraction n1 and n2.
The sphere has radius of curvature R, centered at point C.
The ray from P is incident on the boundary at angle θ1 and
refracts into the second medium at angle θ2
Snell’s Law plus the small angle approximation gives
n1θ1 = n2θ2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 5 / 25
![Page 12: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/12.jpg)
Thin Lenses: Refraction Theory (23.7)
The figure above shows a spherical boundary between two media
with indices of refraction n1 and n2.
The sphere has radius of curvature R, centered at point C.
The ray from P is incident on the boundary at angle θ1 and
refracts into the second medium at angle θ2
Snell’s Law plus the small angle approximation gives
n1θ1 = n2θ2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 5 / 25
![Page 13: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/13.jpg)
Thin Lenses: Refraction Theory (23.7)
The figure above shows a spherical boundary between two media
with indices of refraction n1 and n2.
The sphere has radius of curvature R, centered at point C.
The ray from P is incident on the boundary at angle θ1 and
refracts into the second medium at angle θ2
Snell’s Law plus the small angle approximation gives
n1θ1 = n2θ2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 5 / 25
![Page 14: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/14.jpg)
Thin Lenses: Refraction Theory (23.7)
The figure above shows a spherical boundary between two media
with indices of refraction n1 and n2.
The sphere has radius of curvature R, centered at point C.
The ray from P is incident on the boundary at angle θ1 and
refracts into the second medium at angle θ2
Snell’s Law plus the small angle approximation gives
n1θ1 = n2θ2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 5 / 25
![Page 15: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/15.jpg)
Thin Lenses: Refraction Theory
As usual, we use triangles to determine:
θ1 = α+ φ
θ2 = φ − β
We can use this in Snell’s Law to give
n1(α+ φ) = n2(φ − β)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 6 / 25
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Thin Lenses: Refraction Theory
As usual, we use triangles to determine:
θ1 = α+ φ
θ2 = φ − βWe can use this in Snell’s Law to give
n1(α+ φ) = n2(φ − β)Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 6 / 25
![Page 17: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/17.jpg)
Thin Lenses: Refraction Theory
Use 3 triangles with common side t (see your text) to show
α =ts, β =
ts�,φ =
tR
Plugging these into our new Snell’s Law relationship:
n1
� ts+
tR
�= n2
� tR− t
s�
�
n1
s+
n2
s�=
n2 − n1
R
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 7 / 25
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Thin Lenses: Refraction Theory
Use 3 triangles with common side t (see your text) to show
α =ts, β =
ts�,φ =
tR
Plugging these into our new Snell’s Law relationship:
n1
� ts+
tR
�= n2
� tR− t
s�
�
n1
s+
n2
s�=
n2 − n1
R
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 7 / 25
![Page 19: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/19.jpg)
Thin Lenses: Refraction Theory
Use 3 triangles with common side t (see your text) to show
α =ts, β =
ts�,φ =
tR
Plugging these into our new Snell’s Law relationship:
n1
� ts+
tR
�= n2
� tR− t
s�
�
n1
s+
n2
s�=
n2 − n1
R
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 7 / 25
![Page 20: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/20.jpg)
Thin Lenses: Refraction Theory
Use 3 triangles with common side t (see your text) to show
α =ts, β =
ts�,φ =
tR
Plugging these into our new Snell’s Law relationship:
n1
� ts+
tR
�= n2
� tR− t
s�
�
n1
s+
n2
s�=
n2 − n1
RNeil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 7 / 25
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Thin Lenses: Refraction Theory
Note that this expression is independent of α. All paraxial rays
leaving P converge at P�
Our treatment was developed for a spherical lens which was
convex toward the object point but works for other surfaces as
long as you are careful about the sign convention:
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25
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Thin Lenses: Refraction Theory
Note that this expression is independent of α. All paraxial rays
leaving P converge at P�
Our treatment was developed for a spherical lens which was
convex toward the object point but works for other surfaces as
long as you are careful about the sign convention:
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25
![Page 23: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/23.jpg)
Lenses
We have so-far assumed that all refraction happens at the
mid-point of the lens. Let’s look in detail at what is going on in a
lens.
A lens of thickness t made of material of index n is actually made
of two spherical surfaces of radii R1 and R2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 9 / 25
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Lenses
We have so-far assumed that all refraction happens at the
mid-point of the lens. Let’s look in detail at what is going on in a
lens.
A lens of thickness t made of material of index n is actually made
of two spherical surfaces of radii R1 and R2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 9 / 25
![Page 25: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/25.jpg)
Lenses
We can use our newly derived expressions to write
n1
s+
n2
s�=
n2 − n1
R
1
s1
+ns�
1
=n − 1
R1
The image P� from the first surface becomes the object for the
second surface!
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 10 / 25
![Page 26: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/26.jpg)
Lenses
We can use our newly derived expressions to write
n1
s+
n2
s�=
n2 − n1
R
1
s1
+ns�
1
=n − 1
R1
The image P� from the first surface becomes the object for the
second surface!
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 10 / 25
![Page 27: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/27.jpg)
Lenses
We can use our newly derived expressions to write
n1
s+
n2
s�=
n2 − n1
R1
s1
+ns�
1
=n − 1
R1
The image P� from the first surface becomes the object for the
second surface!
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 10 / 25
![Page 28: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/28.jpg)
Lenses
Remember that virtual images give negative image distances. So,
s2 = t + (−s�1)
Also, at the second surface n1 = n and n2 = 1! So, for the second
surface the equation looks like:
nt − s�
1
+1
s�2
=1 − nR2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 11 / 25
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Lenses
Remember that virtual images give negative image distances. So,
s2 = t + (−s�1)
Also, at the second surface n1 = n and n2 = 1! So, for the second
surface the equation looks like:
nt − s�
1
+1
s�2
=1 − nR2
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 11 / 25
![Page 30: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/30.jpg)
Lenses
Letting t → 0
nt − s�
1
+1
s�2
=1 − nR2
− ns�
1
+1
s�2
= −n − 1
R2
This looks very similar to the equation we obtained for the first
surface. Combining the 2 equations gives
1
s+
1
s�=
1
f(thin lens equation)
and
1
f= (n − 1)
�1
R1
− 1
R2
�(lens −maker�s equation)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 12 / 25
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Lenses
Letting t → 0
nt − s�
1
+1
s�2
=1 − nR2
− ns�
1
+1
s�2
= −n − 1
R2
This looks very similar to the equation we obtained for the first
surface. Combining the 2 equations gives
1
s+
1
s�=
1
f(thin lens equation)
and
1
f= (n − 1)
�1
R1
− 1
R2
�(lens −maker�s equation)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 12 / 25
![Page 32: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/32.jpg)
Lenses
Letting t → 0
nt − s�
1
+1
s�2
=1 − nR2
− ns�
1
+1
s�2
= −n − 1
R2
This looks very similar to the equation we obtained for the first
surface. Combining the 2 equations gives
1
s+
1
s�=
1
f(thin lens equation)
and
1
f= (n − 1)
�1
R1
− 1
R2
�(lens −maker�s equation)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 12 / 25
![Page 33: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/33.jpg)
Lenses
Letting t → 0
nt − s�
1
+1
s�2
=1 − nR2
− ns�
1
+1
s�2
= −n − 1
R2
This looks very similar to the equation we obtained for the first
surface. Combining the 2 equations gives
1
s+
1
s�=
1
f(thin lens equation)
and
1
f= (n − 1)
�1
R1
− 1
R2
�(lens −maker�s equation)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 12 / 25
![Page 34: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/34.jpg)
Lenses
Letting t → 0
nt − s�
1
+1
s�2
=1 − nR2
− ns�
1
+1
s�2
= −n − 1
R2
This looks very similar to the equation we obtained for the first
surface. Combining the 2 equations gives
1
s+
1
s�=
1
f(thin lens equation)
and
1
f= (n − 1)
�1
R1
− 1
R2
�(lens −maker�s equation)
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 12 / 25
![Page 35: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/35.jpg)
Lenses Sign Convention
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 13 / 25
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Image Formation with Spherical Mirrors (23.8)
Curved mirrors can also be used to
form images and are commonly used
in telescopes, searchlights, rearview
mirrors, etc.
A concave mirror has edges which
curve toward the source.
These mirrors also have a focal point
and can form real images.
The lower figure shows how to find
the inverted real image on the same
side of the mirror as the object. Use
the same three pricipal rays we are
used to!
If s > f the image is real and inverted.
Otherwise, a virtual image is formed
behind the mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 14 / 25
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Image Formation with Spherical Mirrors (23.8)
Curved mirrors can also be used to
form images and are commonly used
in telescopes, searchlights, rearview
mirrors, etc.
A concave mirror has edges which
curve toward the source.
These mirrors also have a focal point
and can form real images.
The lower figure shows how to find
the inverted real image on the same
side of the mirror as the object. Use
the same three pricipal rays we are
used to!
If s > f the image is real and inverted.
Otherwise, a virtual image is formed
behind the mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 14 / 25
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Image Formation with Spherical Mirrors (23.8)
Curved mirrors can also be used to
form images and are commonly used
in telescopes, searchlights, rearview
mirrors, etc.
A concave mirror has edges which
curve toward the source.
These mirrors also have a focal point
and can form real images.
The lower figure shows how to find
the inverted real image on the same
side of the mirror as the object. Use
the same three pricipal rays we are
used to!
If s > f the image is real and inverted.
Otherwise, a virtual image is formed
behind the mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 14 / 25
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Image Formation with Spherical Mirrors (23.8)
Curved mirrors can also be used to
form images and are commonly used
in telescopes, searchlights, rearview
mirrors, etc.
A concave mirror has edges which
curve toward the source.
These mirrors also have a focal point
and can form real images.
The lower figure shows how to find
the inverted real image on the same
side of the mirror as the object. Use
the same three pricipal rays we are
used to!
If s > f the image is real and inverted.
Otherwise, a virtual image is formed
behind the mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 14 / 25
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Image Formation with Spherical Mirrors (23.8)
Curved mirrors can also be used to
form images and are commonly used
in telescopes, searchlights, rearview
mirrors, etc.
A concave mirror has edges which
curve toward the source.
These mirrors also have a focal point
and can form real images.
The lower figure shows how to find
the inverted real image on the same
side of the mirror as the object. Use
the same three pricipal rays we are
used to!
If s > f the image is real and inverted.
Otherwise, a virtual image is formed
behind the mirror.Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 14 / 25
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Image Formation with Spherical Mirrors (23.8)
A convex mirror has edges
which curve away from the
object.
The reflected rays appear to
come from inside the mirror
and a virtual image is formed.
The image is upright and
smaller than the real object.
This allows you to have a
wider field of view than you
would have with a flat mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 15 / 25
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Image Formation with Spherical Mirrors (23.8)
A convex mirror has edges
which curve away from the
object.
The reflected rays appear to
come from inside the mirror
and a virtual image is formed.
The image is upright and
smaller than the real object.
This allows you to have a
wider field of view than you
would have with a flat mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 15 / 25
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Image Formation with Spherical Mirrors (23.8)
A convex mirror has edges
which curve away from the
object.
The reflected rays appear to
come from inside the mirror
and a virtual image is formed.
The image is upright and
smaller than the real object.
This allows you to have a
wider field of view than you
would have with a flat mirror.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 15 / 25
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Image Formation with Spherical Mirrors
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 16 / 25
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The Mirror Equation
We have developed a thin-lens equation to calculate the image
location in that system. We can do the same for spherical mirrors
1
s+
1
s�=
1
f, (thin mirror equation)
The focal length of the mirror is related to its radius of curvature:
f =R2
Lateral magnification has the same definition as for a lens
m = −s�
sA similar sign convention exists
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 17 / 25
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The Mirror Equation
We have developed a thin-lens equation to calculate the image
location in that system. We can do the same for spherical mirrors
1
s+
1
s�=
1
f, (thin mirror equation)
The focal length of the mirror is related to its radius of curvature:
f =R2
Lateral magnification has the same definition as for a lens
m = −s�
sA similar sign convention exists
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 17 / 25
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The Mirror Equation
We have developed a thin-lens equation to calculate the image
location in that system. We can do the same for spherical mirrors
1
s+
1
s�=
1
f, (thin mirror equation)
The focal length of the mirror is related to its radius of curvature:
f =R2
Lateral magnification has the same definition as for a lens
m = −s�
s
A similar sign convention exists
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 17 / 25
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The Mirror Equation
We have developed a thin-lens equation to calculate the image
location in that system. We can do the same for spherical mirrors
1
s+
1
s�=
1
f, (thin mirror equation)
The focal length of the mirror is related to its radius of curvature:
f =R2
Lateral magnification has the same definition as for a lens
m = −s�
sA similar sign convention exists
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 17 / 25
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The Simple Magnifier
If you want to see something small,
you bring it close to your eye.
The closest your eye can focus is
called the near point of the eye.
Everybody has a different near point,
it gets less near as you get older.
By convention we specify a standard
near point to be 25 cm.
If you observe something whose
height is h cm at the standard near
point then it subtends an angle
θNP = h/25 cm
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 18 / 25
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The Simple Magnifier
If you want to see something small,
you bring it close to your eye.
The closest your eye can focus is
called the near point of the eye.
Everybody has a different near point,
it gets less near as you get older.
By convention we specify a standard
near point to be 25 cm.
If you observe something whose
height is h cm at the standard near
point then it subtends an angle
θNP = h/25 cm
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 18 / 25
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The Simple Magnifier
If you want to see something small,
you bring it close to your eye.
The closest your eye can focus is
called the near point of the eye.
Everybody has a different near point,
it gets less near as you get older.
By convention we specify a standard
near point to be 25 cm.
If you observe something whose
height is h cm at the standard near
point then it subtends an angle
θNP = h/25 cm
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 18 / 25
![Page 52: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/52.jpg)
The Simple Magnifier
If you want to see something small,
you bring it close to your eye.
The closest your eye can focus is
called the near point of the eye.
Everybody has a different near point,
it gets less near as you get older.
By convention we specify a standard
near point to be 25 cm.
If you observe something whose
height is h cm at the standard near
point then it subtends an angle
θNP = h/25 cm
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 18 / 25
![Page 53: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/53.jpg)
The Simple Magnifier
If you want to see something small,
you bring it close to your eye.
The closest your eye can focus is
called the near point of the eye.
Everybody has a different near point,
it gets less near as you get older.
By convention we specify a standard
near point to be 25 cm.
If you observe something whose
height is h cm at the standard near
point then it subtends an angle
θNP = h/25 cm
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 18 / 25
![Page 54: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/54.jpg)
The Simple Magnifier
If you want to see more detail you
might bring it closer.
but your eye might not be able to
focus it clearly.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 19 / 25
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The Simple Magnifier
If you want to see more detail you
might bring it closer.
but your eye might not be able to
focus it clearly.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 19 / 25
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The Simple Magnifier
If you put a convex lens between your
eye and the object
with the object at or near its focal
point, a distance f from the lens.
you get an image far away or at
infinity.
The image of the object subtends a
greater angle: θ� = h/fthe angular magnification is
θ�
θNP=
25 cm
f
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 20 / 25
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The Simple Magnifier
If you put a convex lens between your
eye and the object
with the object at or near its focal
point, a distance f from the lens.
you get an image far away or at
infinity.
The image of the object subtends a
greater angle: θ� = h/fthe angular magnification is
θ�
θNP=
25 cm
f
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 20 / 25
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The Simple Magnifier
If you put a convex lens between your
eye and the object
with the object at or near its focal
point, a distance f from the lens.
you get an image far away or at
infinity.
The image of the object subtends a
greater angle: θ� = h/fthe angular magnification is
θ�
θNP=
25 cm
f
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 20 / 25
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The Simple Magnifier
If you put a convex lens between your
eye and the object
with the object at or near its focal
point, a distance f from the lens.
you get an image far away or at
infinity.
The image of the object subtends a
greater angle: θ� = h/f
the angular magnification is
θ�
θNP=
25 cm
f
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 20 / 25
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The Simple Magnifier
If you put a convex lens between your
eye and the object
with the object at or near its focal
point, a distance f from the lens.
you get an image far away or at
infinity.
The image of the object subtends a
greater angle: θ� = h/fthe angular magnification is
θ�
θNP=
25 cm
f
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 20 / 25
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The Telescope
fo fe
fo + fe
From FarawayObject
To Final Imageat Infinity
IntermediateImageObjective
Eyepieceo
e
The telescope consists of two pieces: the eyepiece and the
objective. You look through the eyepiece, and you point the
objective towards what you’re looking at.
The objective makes a real image and you look at it with the
eyepiece.
Because we assume the object we’re looking at is at infinity and
the image of it is at, or near, the focal point of the eyepiece, the
image is far away, or at infinity.
The angular magnification is M = −fo/fe.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 21 / 25
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The Telescope
fo fe
fo + fe
From FarawayObject
To Final Imageat Infinity
IntermediateImageObjective
Eyepieceo
e
The telescope consists of two pieces: the eyepiece and the
objective. You look through the eyepiece, and you point the
objective towards what you’re looking at.
The objective makes a real image and you look at it with the
eyepiece.
Because we assume the object we’re looking at is at infinity and
the image of it is at, or near, the focal point of the eyepiece, the
image is far away, or at infinity.
The angular magnification is M = −fo/fe.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 21 / 25
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The Telescope
fo fe
fo + fe
From FarawayObject
To Final Imageat Infinity
IntermediateImageObjective
Eyepieceo
e
The telescope consists of two pieces: the eyepiece and the
objective. You look through the eyepiece, and you point the
objective towards what you’re looking at.
The objective makes a real image and you look at it with the
eyepiece.
Because we assume the object we’re looking at is at infinity and
the image of it is at, or near, the focal point of the eyepiece, the
image is far away, or at infinity.
The angular magnification is M = −fo/fe.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 21 / 25
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The Telescope
fo fe
fo + fe
From FarawayObject
To Final Imageat Infinity
IntermediateImageObjective
Eyepieceo
e
The telescope consists of two pieces: the eyepiece and the
objective. You look through the eyepiece, and you point the
objective towards what you’re looking at.
The objective makes a real image and you look at it with the
eyepiece.
Because we assume the object we’re looking at is at infinity and
the image of it is at, or near, the focal point of the eyepiece, the
image is far away, or at infinity.
The angular magnification is M = −fo/fe.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 21 / 25
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The Microscope
fe
intermediate real image
virtual image25 cm to ! away
eyepiece objective
fe fo fo
object
L
qo
The microscope also consists an objective and eyepiece
The difference from the telescope is that the object is very close to
the focal point of the objective.
But, like the telescope, the image it forms is near the focal point of
the eyepiece.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 22 / 25
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The Microscope
fe
intermediate real image
virtual image25 cm to ! away
eyepiece objective
fe fo fo
object
L
qo
The microscope also consists an objective and eyepiece
The difference from the telescope is that the object is very close to
the focal point of the objective.
But, like the telescope, the image it forms is near the focal point of
the eyepiece.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 22 / 25
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The Microscope
fe
intermediate real image
virtual image25 cm to ! away
eyepiece objective
fe fo fo
object
L
qo
The microscope also consists an objective and eyepiece
The difference from the telescope is that the object is very close to
the focal point of the objective.
But, like the telescope, the image it forms is near the focal point of
the eyepiece.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 22 / 25
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The Microscope
fe
intermediate real image
virtual image25 cm to ! away
eyepiece objective
fe fo fo
object
L
qo
From analysing the geometry we find that the angular magnification is
M ≈ −L 25 cm
fofe.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 23 / 25
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Vision (24.3)
A Poet: the eyes are the window to the soul
A Physicist: an eye is a fluid-filled ball about 2.3cm in diameter
Let’s talk about the optical properties of that ball.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 24 / 25
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Vision (24.3)
A Poet: the eyes are the window to the soul
A Physicist: an eye is a fluid-filled ball about 2.3cm in diameter
Let’s talk about the optical properties of that ball.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 24 / 25
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Vision (24.3)
A Poet: the eyes are the window to the soul
A Physicist: an eye is a fluid-filled ball about 2.3cm in diameter
Let’s talk about the optical properties of that ball.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 24 / 25
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Vision
The cornea is transparent and sharply curved. It works with the
lens to provide the refractive power of the eye.
The fluid has n = 1.34 (like water). The lens has n = 1.44
The pupil is a variable-diameter aperture in the iris. It can adjust
from ≈ 1.5mm to ≈ 8mmThe light detector is the retina, which has rods for light and dark
and cones for colour.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 25 / 25
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Vision
The cornea is transparent and sharply curved. It works with the
lens to provide the refractive power of the eye.
The fluid has n = 1.34 (like water). The lens has n = 1.44
The pupil is a variable-diameter aperture in the iris. It can adjust
from ≈ 1.5mm to ≈ 8mmThe light detector is the retina, which has rods for light and dark
and cones for colour.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 25 / 25
![Page 74: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/74.jpg)
Vision
The cornea is transparent and sharply curved. It works with the
lens to provide the refractive power of the eye.
The fluid has n = 1.34 (like water). The lens has n = 1.44
The pupil is a variable-diameter aperture in the iris. It can adjust
from ≈ 1.5mm to ≈ 8mm
The light detector is the retina, which has rods for light and dark
and cones for colour.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 25 / 25
![Page 75: Physics 121: Optics, Electricity & Magnetism · Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 8 / 25. Lenses We have so-far assumed that all](https://reader030.vdocuments.site/reader030/viewer/2022040614/5f0a75cf7e708231d42bbe33/html5/thumbnails/75.jpg)
Vision
The cornea is transparent and sharply curved. It works with the
lens to provide the refractive power of the eye.
The fluid has n = 1.34 (like water). The lens has n = 1.44
The pupil is a variable-diameter aperture in the iris. It can adjust
from ≈ 1.5mm to ≈ 8mmThe light detector is the retina, which has rods for light and dark
and cones for colour.
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 25 / 25