Ch7 geom optics sept13

Geometrical OpticsImages Formed by Plane Mirrors, Images Formed by Spherical MirrorsImages Formed by Refraction, LensesLens Aberrations The cameraThe simple magnifierThe compound microscope, The telescopeIllumination and Brightness

Images Formed by Plane Mirrors

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Concave Mirror

Images Formed by Spherical Mirrors

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Locating images

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Convex Mirror

Parallel rays striking a convex spherical mirror are reflected as if coming from a single point behind the mirror

The images formed by a convex spherical mirror are always virtual, upright, smaller and between the mirror and F

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- Mirror equationSince therefore

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For small angles (paraxial rays):

Image formed by refraction

(An exterior angle of any triangle equals the sum of the two opposite interior angles)

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For surface 1: For surface 2:

Image for surface 1 is object for surface 2

Assuming t small p2 = -q1, Adding,

For thin lens, distances measured from centre plane,

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LENSMAKER’S EQUATIONFor thin lenses in air,

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111

1

RRn

f

Where, f is focal length of lens and n is refractive index of material. Radius of curvatureR { +ve for convex surfaces -ve for concave surfaces

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(Any two rays would suffice; the point of intercept would determine the position of the image)

Thin lensesConvex lens

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Locating Images by Ray Tracing

Object more than F.Image characteristics:

Concave lens

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Angle AFB = angle IFI’ and AB = ho,

Triangles OAO’ and IAI’ are similar,

Equate the right sides,

Lens equation

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Lenses in contact:

2nd lens:

1st lens:

Adding: Therefore

Image formed by 1st lens becomes object for 2nd lens

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Lens Aberrations

Spherical aberration occurs because the focal points of rays far from the principal axis of a spherical lens (or mirror) are different from the focal points of rays of the same wavelength passing near the axis.Correction?

A material’s index of refraction varies with wavelength. Because of this phenomenon, violet rays are refracted more than red rays when white light passes through a lens.Correction? Badrul hisham Nov 13 24