Download Physics 11 OPTICS Concave and Convex Lenses What is a lens

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Physics 11 Block: _____ Date: _______________
OPTICS
Concave and Convex Lenses
What is a lens?
•
A lens is carefully ground or moulded piece of TRANSPARENT MATERIAL that REFRACTS light
rays in such a way as to form an image.
•
At the geometric centre of any lens is a point called the OPTICAL CENTRE (O) as opposed to the
vertex with mirrors.
•
Unlike curved mirrors, a lens does not have a RADIUS OF CURVATURE. Instead, they have a point
called 2F POINT, located at TWICE THE FOCAL LENGTH.
•
The same side of the object is known as VIRTUAL; the side of the image is known as REAL.
•
Since you can see from both sides of a lens, F and 2F exists twice.
o F and 2F represent the REAL principal focus, located on the side of the image.
o F’ and 2F’ represent the VIRTUAL principal focus, located on the side of the object.
•
All other parts are the same with curved mirrors.
•
There are 2 types of lenses:
o Convex or CONVERGING lenses
o Concave or DIVERGING lenses
Figure 1 – Converging rays with a convex lens and diverging rays with a concave lens.
Physics 11 Ray diagrams for convex (converging) lenses:
There are 3 rules:
1. An incident ray that is PARALLEL to the principal axis is refracted through the F. (See Figure 2A)
2. An incident ray that passes through the F’ is refracted PARALLEL to the principal axis. (See Figure 2B)
3. An incident ray that passes through the OPTICAL CENTRE goes straight through and does not refract.
(See Figure 2C)
Figure 2
The images you get from a convex lens are exactly the same as those from a CONCAVE mirror (both are
converging). Therefore, the steps for drawing ray diagrams are exactly the same.
Let’s try some ray diagrams for convex lenses.
Example 1 – Real Image
è
Characteristics of image:
Opposite side, between F and 2F; inverted; reduced; real
*There are a total of 6 cases where a convex lens produces real images.
Physics 11 Example 2 – Virtual Image
è
Characteristics of image:
Same side, farther from object; upright; magnified; virtual
*There is only 1 case where a convex lens produces a virtual image, when object is closer to the lens than F’.
Ray diagrams for concave (diverging) lenses:
For a concave lens, light rays are refracted such that they RADIATE from the F’ (virtual focus).
Otherwise, the same 3 rules apply.
Figure 3
The images you get from a concave lens are exactly the same as those from a CONVEX mirror since both are
diverging.
Physics 11 Example 3 – Virtual Image
è
Characteristics of image:
Same side, nearer than object; upright; reduced; virtual
The Mirror/Lens & Magnification Equations
The mirror/lens equation can be used to find the characteristics (L. O. S. T.) of the OBJECT or IMAGE when
combined with the magnification equation.
1 1 1
=
+
f do di
M=
hi
d
=− i
ho
do
[From before]
where:
M = MAGNIFCATION (NO UNITS)
*A ratio of the image’s height to the object’s height
Physics 11 Example 4 – An object 2.25 mm high is 8.5 cm to the left of a convex lens with 5.5 cm focal length. Find the
image location and height.
*Object is located between F’ and 2F’. Therefore, image is real (opposite side of lens)
ho = 2.25mm = 0.225cm
do = 8.5cm
f = 5.5cm
1 1 1
= +
f do di
1 1 1
= −
di f do
1
1
1
=
−
= 0.06417
di 5.5 8.5
di = 15.58cm
hi
d
=− i
ho
do
hi = −
di × ho
(15.58) × (0.225)
=−
= −0.4125cm
do
(8.5)
The image is located 16 cm from the lens, on the opposite side of the object, and is inverted. It is 0.41 cm
or 4.1 mm tall.
Example 5 – A stamp collector wants to magnify images exactly 4 times when the object is 3.5 cm from
the lens. What focal length lens is needed?
M = 4.00
do = 3.5cm
hi = 4.00ho ⇒ di = −4.00do = −4.00(3.5) = −14cm
f =?
1 1 1
= +
f d o di
1
1
1
=
+
= 0.2143
f −14 3.5
f = 4.7cm
Physics 11 A summary table of curved mirrors and lenses:
Convex Mirror / Concave
Lens
Concave Mirror / Convex Lens
f
focal length
–
(always)
+
(always)
do
object distance
+
(always)
+
(always)
ho
object height
+
(always)
+
(always)
Virtual image
(always)
Virtual image
di
image distance
–
–
+
hi
image height
+
(upright)
+
(upright)
–
(inverted)
M
magnification
+
(upright)
+
(upright)
–
(inverted)
Real Image
For convex/concave mirrors:
è
di is + if the image is located on the object's side of the mirror, and/or if it’s a real image.
è
di is – if the image is located behind the mirror, and/or if it’s a virtual image.
For convex/concave lenses:
è
di is + if the image is a real image and located on the opposite side of the lens.
è
di is – if the image is a virtual image and located on the object's side of the lens.