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PRESENTED BY: ARJEL A. DIONGSON SPHERICAL MIRROR EQUATION SPHERICAL ABERRATION

spherical mirror equation

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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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Page 1: spherical mirror equation

PRESENTED BY:

ARJEL A. DIONGSON

SPHERICAL MIRROR EQUATION

SPHERICAL ABERRATION

Page 2: spherical mirror equation

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.

Page 3: spherical mirror equation

SPHER

ICAL

MIR

ROR EQ

UATIO

N

Page 4: spherical mirror equation

DERIVATION OF SPHERICALMIRROR EQUATION

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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

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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

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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

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Multiplying both sides of this equation by do gives

dof do - f

Spherical Mirror

Equation in different form

DERIVATION OF SPHERICALMIRROR EQUATION

di

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MAGNIFICATION FACTOR

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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.

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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

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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.

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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:

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SPHERICAL ABERRATION

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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.

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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.

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SPHERICAL MIRROR VSPARABOLIC MIRROR

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APPLICATIONS OF SPHERICAL MIRRORS

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