Reflection in Curved Mirrors
Description of Spherical Mirror
- Downloadable handout - Curve
Mirror
- An ideal Curved mirror would have the shape of a parabola. One
of the properties of a parabola is that parallel rays will reflect
directly to one focal point.
- In reality parabolic mirrors (and lenses) are expensive to
produce and therefore rarely used. Instead a spherical mirror
usually utilized. A problem is that all parallel rays on a
spherical mirror do not focus on a single point. This problem is
known as spherical aberration.
- If the size of a spherical mirror is small compared to its
radius of curvature then the rays can be approximated to come to a
single focal point, and the focal length of the mirror is 1/2 of
the radius of curvature.
- vocabulary
- principal axis
- focal length
Rules for Producing Images in Spherical Mirrors
- Rays parallel to the principal axis will reflect through the
focal point.
- Rays traveling through the focus will reflect back parallel to
the principal axis.
- Rays passing through the centre of curvature will reflect back
on themselves. (A line from the centre of curvature to the mirror
is normal to the mirror surface)
- A ray striking the intersection of the principal axis and the
mirror surface will reflect back with an angle of reflection equal
to the angle of incidence. (as measured from the normal which in
this case is the principal axis)
Magnification in Spherical Mirrors
- Downloadable handout - Curve
Mirror
- Can be derived using similar triangles from a ray diagram
- M= hi/ho (by definition) (M - magnification, hi - height of
image, ho - height of object)
- M= - di/do (- is placed as a sign convention ( a negative
magnification indicates an inverted image, a positive
magnification indicates a non inverted image) di - distance of
the image from the mirror, do - distance of the object from the
mirror)
Images in Concave Mirrors
- Downloadable handout - Concave
Mirror
- Determine the characteristics of images formed in a concave
mirror in the following cases
- Case 1 - Object is beyond C (centre of curvature)
- Case 2 - Object is between C and the focal point F
- Case 3 - Object is between F and the mirror surface
- In each case determine the orientation, magnification and type
of image
Images in Convex Mirrors
Questions
- A 20 mm high object is placed 120 mm in front of a concave
mirror which has a radius of curvature of 100 mm. (i) determine
the characteristics of the image formed, (ii) determine from a ray
diagram drawn to scale the distance di. (the distance from the
image to the intersection of the mirror and the PA), (iii)
calculate the height of the image hi.
- For a concave mirror, an object is 20 cm high, the radius of
curvature of the mirror is 100 cm, and the distance to the object
do is 90 cm. If the height of the image is 24 cm, then what is the
distance to the image, di?
- A stainless steel sphere in front of NRC Corporate Services on
Montreal Road in Ottawa was sculpted by Canadian Arthur Price as a
symbol of excellence and represents knowledge. It was commissioned
in 1966 to celebrate the 50th anniversary of the NRC. A rabbit 150
mm high looks at itself at a distance of 5 m from the ball, what
would be the characteristics and height of its image be? Assume
the radius of curvature is 1.0 m.
- A student is walking toward a large concave spherical mirror
at a fair in the "house of mirrors". As the student is walking
toward the mirror it is noticed that the image changes from
inverted to upright at a location 5 m from the mirror. What is the
radius of curvature of the mirror?
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