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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.