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this slide includes the derivation of spherical mirror equation, lateral magnification, spherical aberration of mirrors and the difference between spherical and parabolic mirrors..
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PRESENTED BY:
ARJEL A. DIONGSON
SPHERICAL MIRROR EQUATION
SPHERICAL ABERRATION
To derive spherical mirror equation;
To solve problems using Spherical Mirror Equation;
To explain Spherical Aberration of Mirrors;
Appreciate the importance of spherical mirrors through citing its applications in the society.
SPHER
ICAL
MIR
ROR EQ
UATIO
N
DERIVATION OF SPHERICALMIRROR EQUATION
O’AO and I’AI are similar, since their angles at A are equal. Hence we can write
hi di
ho do
DERIVATION OF SPHERICALMIRROR EQUATION
The (focal) ray through F also forms similar triangles, O’FO and AFB.
The bases of these triangles are AF = f and OF = do - f .
DERIVATION OF SPHERICALMIRROR EQUATION
Then, if VA is taken to be hi,
hi AF f ho OF do – f From equations
1 & 2, we have di f do do - f
DERIVATION OF SPHERICALMIRROR EQUATION
Multiplying both sides of this equation by do gives
dof do - f
Spherical Mirror
Equation in different form
DERIVATION OF SPHERICALMIRROR EQUATION
di
MAGNIFICATION FACTOR
MAGNIFICATION FACTORLateral Magnification, also called
magnification factor is the ratio of the height of the image (hi) to the
height of the object (ho) – that is hi
ho
where the minus sign is inserted as a convention.
M di
dO
HERE IS HOW THIS WORKS:•If we get a POSITIVE magnification, the image is UPRIGHT.•If we get a NEGATIVE magnification, the image is INVERTED •If the magnification value is GREATER than 1, the image is ENLARGED.•If the magnification value is LESS than 1, the image is REDUCED.•If the magnification value is EQUAL to 1, the image is the SAME SIZE as the object.
SIGN CONVENTION FOR SPHERICAL MIRRORS
SIGNS FOCAL LENGTH
(f )
IMAGE DISTANCE
(di)
OBJECT DISTANCE
(do)
IMAGEORIENTATION
(M)
Concave (converging)
mirror
When the image is formed in front of the
mirror (real image)
When the object is in front of the
mirror (real object)
When the image is upright with respect
to the object
Convex (converging)
mirror
When the image is formed
behind the mirror
(virtual image)
When the object is behind the
mirror (virtual object)
When the image is inverted with
respect to the object
Sample Problem: # 1A Concave mirror has a radius of curvature of 30cm. If an object is placed at 20cm from the mirror, where is the image formed and what is its characteristics? (Specify real or virtual, upright or inverted, and larger or smaller for the image).
Given: R= 30cmdo = 20cm
Req’d: di = ?
Solution: f = =
= 15cm
R2
30cm
2
dof (20cm)(15cm)
do – f 20cm – 15cm
300cm2 5cm
di
60cm
di 60cm do 20cm
M
-3.0
In this case, the image is real, inverted, and 3 times the size of the object.
Sample Problem: # 2An object is 30cm in front of a diverging mirror that has a focal length of 10cm. Where is the image, and what is its characteristics?
Given:
Req’d:
Solution:
SPHERICAL ABERRATION
SPHERICALABERRATION
An optical effect observed in an optical device (lens, mirror, etc.) that occurs due to the increased refraction of light rays when they strike a lens or a reflection of light rays when they strike a mirror near its edge, in comparison with those that strike nearer the center.
Signifies a deviation of the device from the norm, i.e., it results in an imperfection of the produced image.
The farther the incident ray from the axis,
the more distant is its reflected ray from the focal
point.
SPHERICALABERRATION
According to the small angle approximation, rays parallel to and near the mirror’s axis converge at the focal point. However, when parallel rays not near the axis are reflected, the converge in front of the focal point giving rise to blurred images.
The farther the incident ray from the axis,
the more distant is its reflected ray from the focal
point.
SPHERICAL MIRROR VSPARABOLIC MIRROR
APPLICATIONS OF SPHERICAL MIRRORS