1285140343 6.Phy ImpFormulaeBasicConcepts RayOpticsWaveOptics Ch9100

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Transcript of 1285140343 6.Phy ImpFormulaeBasicConcepts RayOpticsWaveOptics Ch9100

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    Important formulae & basic concepts

    Chapter: Ray Optics & Optical instruments & Wave Optics

    XII Physics

    All distances are measured in meter (m)

    Snells law statesn = sin i/ sin r

    n is refractive indexi is the angle of incidencer is the angle of refraction

    Sign convention distances measured in the same direction incident light is positiveDistances measured in the opposite directi

    is negativeAll distances are measured from the pole

    Mirror equation1 1 1

    v u f+ =

    u is object distance; v is image distance anf is focal length

    Sign of focal length of mirror f is negative for concave mirror;f is positive for convex mirror

    Magnification of a spherical mirrorm = -v/u

    m is positive then image is erect; m isnegative then image is inverted

    For prism 2 m211

    n sin[(A D ) /2]n

    n sin(A /2)

    += =

    n2 is refractive index of prism material

    n1 is refractive index of surrounding mediu

    A is the angle of prismDm is the angle of minimum deviation

    For spherical interface

    2 1 2 1n n n n

    v u R

    =

    n1 is refractive index to the left of therefracting surface

    n2 is refractive index to the right of therefracting surface

    Thin lens formula1 1 1

    v u f =

    u is object distance(m); v is image distancand f is focal length

    Distances measured in the same direction incident light is positiveDistances measured in the opposite directi

    is negativeAll distances are measured from the optica

    centre

    Lens makers formula

    2 1

    1 1 2

    (n n )1 1 1

    f n R R

    =

    R1 and R2 are the radii of curvature of the

    lens surfacesn2 is the r.i. of the lens and n1 is the r.i. of

    surrounding medium

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    Power of lens

    P = 1/f

    Power is positive for a converging lens;

    negative for diverging lens. Unit: dioptre(D

    Power of combination of lenses

    1 2 3P P P P ...= + + +

    Magnifying power of a simple microscope Dm 1

    f= + for object at least distance of

    distinct vision

    Dm

    f= if image is at infinity

    Magnifying power of a compoundmicroscope

    O e

    O

    e

    L Dmf f

    f is focal length of objective

    f is focal length of eye lens

    =

    Magnifying power of a telescopeO

    e

    fm

    f=

    O

    e

    f is focal length of objective

    f is focal length of eye lens

    Wavelength of light in a medium ofrefractive index n is

    n

    n

    =

    n is the refractive index of the medium

    n

    is the wavelength of incident light

    is the wavelength of refracted light

    Youngs double slit experiment ,conditions for maximum and minimum

    intensity are

    dsin m for m = 0, 1, 2,... for bright frin

    dsin (m 1/2) for m = 0, 1, 2,... for da

    =

    = +

    d is the distance between the slits

    is the angle the light path makes with the

    central axis

    Youngs double slit experiment

    Fringe width is Dd

    =

    D is the distance of the slits from the scree

    d is the distance between the slitsis the wavelength of incident light

    Angular width of fringes isd

    Diffraction at a single slit of width a giveszero intensity at angles of

    2 3, ,

    a a a

    etc.

    is the wavelength of incident light

    a is the width of the slit

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    Secondary maximas are at

    3 50, ,

    2a 2a

    etc.

    Resolving power of a microscope is the

    reciprocal of minimum separation of twopoints (dmin) to be seen as distinct.

    min

    1 2nsinResolving power =

    d 1.22

    =

    n is r.i. of medium between the object and

    objective lensis the wavelength of incident light

    2 is the angle subtended by the diameter

    of objective lens at the focus of the micros

    Fresnel distance is the distance beyondwhich spread of the beam due todiffraction is more than the size a of the

    slit is significant.2az =

    is the wavelength of incident light

    a is the width of the slit

    Brewsters law states that

    Bn tani=

    The angle of incidence iB is called Brewster

    angle.

    Malus law states that the intensity of

    transmitted light is 20I I cos=

    I0 is the intensity of initially unpolarized lig

    and is the angle between the polarizationdirection of the original light and the

    polarizing direction of the sheet.