Goal: To understand how
mirrors and lenses work
Objectives:
1)
To understand how Plane mirrors create an
image
2)
To understand how Convex Mirrors reflect light
3)
To understand the properties of Concave Mirrors
4)
To be able to calculate the Focal Length and
Magnification of a lens or mirror
5)
To understand the similarities of Lenses and
Mirrors
Plane mirrors
• These are the sort of mirrors you find in a
bathroom.
• They are straight and flat.
Convex mirrors
• Convex Mirrors curve away from you.
Concave Mirrors
• Convex mirrors curve towards you
Some basic properties
• Object distance.
• This is denoted as p.
• This is the physical distance the object is
away from the mirror.
• Radius of Curvature (C) is what the radius
of a mirror would be if it was an entire
sphere.
Image distance and focal length
• This is the distance the image appears to
be away from the mirror (denoted q).
• Focal length (denoted f) is the distance
from the mirror to the focal point (where all
the light would come together for a light
source very far away).
Mirror Equation
• Finally some math…
• 1/p + 1/q = 1/f
• Yes, you can use that trick I showed you
earlier with this!
• So, f = pq / (p+q)
• And p = -fq / (f – q)
• The minuses due to 1/p = 1/f – 1/q
Sample
• An object is place 5 cm away from a mirror
which has a focal length of 2 cm.
• What is the distance from the mirror to the
image?
Sample
• An object is place 5 cm away from a mirror
which has a focal length of 2 cm.
• What is the distance from the mirror to the
image?
• q = (on board)
• Note that a negative means that the image is a
virtual image (is in front of the mirror).
• Positive values of q mean real image (behind
the mirror).
• p is always positive
Another
• An object is 10 cm away from a mirror.
• The image in the mirror is 5 cm behind the
mirror.
• A) is this a real or imaginary image?
• B) what is the focal length of the mirror?
Magnification
• m = h’ / h
• That is it is the height of the image divided by
the height of the actual object.
• Also, m = -q / p
• Note that when q is positive (real image) m is
negative.
• This means that the image is inverted (upside
down).
• What would be true about the image if q is
negative?
Lenses
• There are two types of lenses.
• Diverging lenses make light spread out.
• Diverging lenses tend to be concave.
• Not that q and f are BOTH negative for a lens or
mirror that is diverging.
• Converging lenses make light focus on a point.
• Converging lenses tend to be convex.
Diverging vs converging
• Diverging (concave) lenses generate an
image in front of the lens.
• Is this a real or virtual image?
Diverging vs converging
• Diverging (concave) lenses generate an
image in front of the lens.
• Is this a real or virtual image?
• Virtual image
• Since you have a virtual image, is q going
to be positive or negative?
Diverging vs converging
• Diverging (concave) lenses generate an image
in front of the lens.
• Is this a real or virtual image?
• Virtual image
• Since you have a virtual image, is q going to be
positive or negative?
• Negative!
• Since q is negative will the magnification be
positive or negative?
Diverging vs converging
• Diverging (concave) lenses generate an image
in front of the lens.
• Is this a real or virtual image?
• Virtual image
• Since you have a virtual image, is q going to be
positive or negative?
• Negative!
• Since q is negative will the magnification be
positive or negative?
• Positive (upright image)
Converging lens
• q is usually, but not always positive.
• This means the magnification will be
negative (inverted image).
•
•
•
•
However, q can be negative
q = -fp / (f – p)
So, if f is > p then q is actually negative.
That is if the object is closer to the lens
than the focal length you get a virtual
image – otherwise you get a real image.
Conclusion
• We learned about the different mirror and
lens types.
• We learned how to find object distance,
image distance, and focal length.
• We learned 2 ways to calculate
magnification.
• We learned the differences between real
and virtual images and how they translate
to inverted or upright images.