Ray Optics And Optical Instruments Class 12 Notes Physics Chapter 9 - CBSE

What are Ray Optics and Optical Instruments ?

 Topic Formula Symbol Representation Important Points Apparent Depth Apparent depth = (real dept/µ) µ=refractive index=(sin i/sin r)(Snell's law)i = incident angle of rayr = angle of refraction When we look into a pool of water, the bottom of the pool will appear to be raised due to refraction of light. Critical Angle c = sin-1(1/µ) or μ = (1/sin c) μ = refractive index of denser medium w.r.t. rarer mediumc = critical angle which depends on colour of light Phenomenon of refraction of light into denser medium from the boundary of denser medium with rarer medium known as total internal reflectionsi > icSome of the important applications of total internal reflection:(a) Diamond brilliance(b) Optical fiber(c) Mirage Lens Maker’s Formula (1/f)=(µ-1) ( (1/R1)-(1/R2)) μ = refractive index of material of lens w.r.t. medium in which lens is placed.R1, R2 = radii of curvature of the two surfaces of the lens. This formula is valid for all types of lenses. Thin Lens Formula (1/v)-(1/u) =( 1/f) u = distance of the object from the optical centre of the lens v = distance of image from the optical centre of the lensf = focal length of the lens f is positive for converging or convex lens and negative for diverging or concave lens. Linear Magnification m=(I/O)-(V/U) v = size of imageu = size of object m is positive for virtual image and m is negative for real image.
 Topic Formula Symbol Representation Important Points Power of a Lens P = (1/f) f = focal length in metres Unit of power of lens = dioptre= 1D= 1m-1 • Ability of lens to converge or diverge a beam of light.• P is positive for a convex lens and negative for a concave lens.• When focal length of a lens is in cm, then P =(100/f(in cm))dioptre Combination of then lenses •(1/F1)+(1/F2)+(1/F)• P = P1 + P2• m = m1 × m2 F1, F2 = Focal length of two thin lenses places coaxiallyF = focal length of combinationP = Power of lens with proper signm1, m2 = magnification Combination of lens used for:• Increase the magnification of image• Make the final image erract w.r.t. object• Reduce certain observations Angle of deviation δ = i1 + i2 – A i1 = angle of incidencei2 = angle of emergenceA = r1 + r2 = angle of prism The difference between the sum of incident angles and the sum of emergent angles is known as the angle of deviation. Prism Formula μ = sin[(A+δm)/2]/sin(A/2)(Snell’s law) A = angle of prismδm= angle of minimum deviationi = angle of incidenceδm = 2 i – Awhen i1 = i2and r1 = r2 • For thin prism,Sin [A+δm]/2→(A+δm/2) and Sin (A/2)→(A/2)• δ = (μ–1)A this is the formula of angle of maximum deviation. Angular Dispersion θ = δV – δR= (µV – μR) A δV, δR = Deviation of violet and red lightμV, μR = Refractive index for violet and Red colour. The difference in the angle of deviation between two extreme colours is known as angle of dispersion or angular dispersion for the two colours. Magnifying Power of Simple Microsope • Image, at the least distance of vision m=1+(D/f)• Image at infinity m=(D/f) m = magnification D = least distance vision A simple microscope or a simple magnifying glass is a converging lens of small focal length. Magnifying Power of Compound Microscope • Image, at infinity m=(-L/v0(D/fe))• Image, at the least distance of visionm =(-Vo/Uo(1+(D/fe)) uo = distance of object from the objective lensvo=L=distance of image from the objective lens (length of microscope tube)fe = focal length of the eye lensD = least distace of distinct vision. • Compound microscope is the combination of two convex lenses one compounding the effect of the other, for much larger magnification.• The objective have smaller aperture and smaller focal length than the eye-piece.
 Topic Formula Symbol Representation Important Points Mirror Formula (1/u)+(1/v)=(1/f) u = distance of object from the pole of the mirrorv = distance of imagef = (R/2) • Mirror formula is same for both concave and convex mirrors equation remain uneffected whether the image is real or virtual. Linear Magnification • m =(size of image (h2)/size of object (h1)) • m =(f/f-v) f = focal length of magnifying lens. In case of concave mirror, when image is real,m = negative.When image is virtual, m is positive. Use of spherical mirror • As reflector in street lamps, search light.• Driving mirror• Telescopes, solar cookers Optical fiber • Based on total internal reflection.• Use for data transmission using light pulses. • Made of plastic or glass. Magnifying Power Astronomical Telescope (Refracting Type) • When the final image is formed at infinity (Normal Adjustment), m=(fo/fe)• When the final image is formed at least distance of distinct vision,m =(-fo/fe)(1+(fe/D)) fo = Focal length of objective lensfe = Focal length of the eye-pieceD = least distance of distinct vision (i.e. 25 cm) • Astronomic telescope (Refracting type) is consist of two converging lense the objective lens has large focal length and large aperture than the eye-piece. Magnifying Power of Reflecting Type Telescope In normal adjustmentm =(-fo/fe)=((R/2)/fe) R = radius of curvature of concave mirror • It is improvement over refracting type telescope. Here, the objective lens is replaced by a concave parabolic mirror.