2 mark. 4 mark. Physical Optics PC 1 Electrostastics T/P 1 C Current Electricity. Atomic Physics T/P 4 1 C TOTAL

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2 TOPIC 1 mark Geometrical Optics 2 mark 4 mark 5 mark theory 5 mark problem C Physical Optics PC 1 Electrostastics T/P 1 C Current Electricity T/P 2 1 C Atomic Physics T/P 4 1 C TOTAL

3 Laws of refraction n 1 sin i = n 2 sin r

4 LATERAL SHIFT When a ray of light is incident obliquely on a parallel sided glass slab the emergent ray shifts laterally. The perpendicular distance between the direction of the incident ray and emergent ray is called lateral shift.

5 P N` A i Q r i-r T B t D N R C S

6 ABCD=Principal section of a glass slab PQ = incident ray QR = refracted ray RS = emergent ray NN`= normal RT = lateral shift BC = t = thickness of the slab i = angle of incidence r = angle of refraction

7 Consider NQR,cos r = From the QRT,sin(i-r)= QN QR RT QR QN QR= cos r RT cos r QN

8 t NORMAL SHIFT The apparent shift in the position of an object placed in one medium and viewed along the normal, from the other medium. N` N I O r i S P i R r Q

9 OP = incident ray PQ = refracted ray produced backwards meet ON at I NN`= normal OI = normal shift RPO = i = angle of incidence = NPO QPS = r = angle of refraction = NIP t = thickness of the optical medium From the NPO From the NPI

10 n 1 sin i = n 2 sin r Here n 1 = n n 2 = 1 P is a point which very close to N

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12 TOTAL INTERNAL REFLECTION r 90 0 i C i>c denser medium

13 REFRACTION THROUGH A PRISM A Z i1 Q r1 M d r2 R i1 P N S B C

14 ABC = principal section of the prism BC = Base A = Angle of the prism PQ = Incident ray QR = Refracted ray RS = Emergent ray ZMS = d = Angle of deviation i 1 = Angle of incidence r 1 = Angle of refraction r 2 = Angle of incidence at the face AC i 2 = Angle of emergence

15 Consider the Quadrilateral AQNR In the ΔQNR A + QNR = r 1 + r 2 + QNR = equating the above two equations, we have A + QNR = r 1 + r 2 + QNR A = r 1 + r (1) d = (i 1 r 1 ) + (i 2 r 2 ) d = (i 1 + i 2 ) (r 1 + r 2 ) = i 1 + i 2 - A (from 1) d + A = i 1 + i (2)

16 at minimum deviation i 1 = i 2 = i r 1 = r 2 = r d = D (1) A = 2r or r = A/2 (2) D + A = 2i or i = (A+D)/2 d d D i i 1 i 2 i

17 REFRACTION THROUGH CURVED SURFACES Curved surface: It is a part of a sphere. Principal axis: The horizontal line passing through the centre of the curved surface. Pole(P): Centre of the curved surface. Centre of curvature(c): It is a point on the principal axis which is the centre of the sphere in which curved surface is a part.

18 Principal focus(f): It is a point on the principal axis where parallel rays from infinity converge or appear to diverge from that point Focal length (f): It is the distance between the principal focus and the pole. Radius of curvature(r): It is the distance between centre of curvature and the pole

19 Relation between n,u,v&r i N r M ϴ C O I P

20 OM = incident ray MN = refracted ray MI = refracted ray produced backwards CP = radius of curvature (R) OP = object distance (u) IP = image distance (v) i = angle of incidence r = angle of refraction

21 Applying sine rule to the s CMO & CMI Dividing equation (2) by equation (1)

22 = X = We know that n 1 sin i = n 2 sin r =

23 Dividing the above equation through out by uvr

24 M is a point which is very close to P, therefore IM IP = -v (because image is virtual) OM OP = u CO = CP OP = R - u CI = CP - IP = R + v

25 Lens maker s formula A E F O P B D u v I V` I` C

26 OE = incident ray FI = refracted ray O = point object I` = virtual object for the surface ADC OP = u =object distance R 1,R 2 =radii of curvatures of the surfaces ABC and ADC PI =v=image distance P I` =v` =image distance for the first surface

27 For the refraction through surface ABC, For the refraction through surface ADC, Negative sign indicates that the object is virtual

28 Adding (1) and (2)

29 Two thin lenses in contact L1 L2 O I I` u v V`

30 Let us consider two thin lenses in contact let f 1 and f 2 be their focal lengths let u=object distance v =image distance v`=virtual image distance For refraction through first lens, here I` is the image formed

31 For refraction through second lens, here I` serves as virtual object for the second lens. Adding equations (1) and (2)

32 let F be the effective focal length of the combination.

33 Questions carrying ONE mark each 1. Define critical angle. 2. Mention an application of total internal reflection. 3. What is dispersion of light? 4. Write the expression for the deviation produced by a thin prism. 5. Define dispersive power of the material of a prism. 6. What is angular dispersion? 7. Write the condition for dispersion without deviation.

34 8. Define power of a lens. 9. What is magnification? 10. Write the relation between power and focal length of a lens. 11. Write the expression for the equivalent focal length of two thin lenses separated by a distance. 12. What is a thin prism? 13. What is the lateral shift produced by a parallel sided glass slab for grazing incidence of light? 14. A thin convex lens of focal length 0.1m & a thin concave lens of focal length 0.1m are placed coaxially in contact. What is the net power of the combination?

35 Questions carrying two marks 1.Mention the conditions for total internal reflection to occur. the light ray should travel from denser medium to rarer medium the angle of incidence must be greater than critical angle 2.Arrive at the relation between critical angle and refractive index. c Here n 1 =n, i=c, n 2 =1 & r=90 0 n sinc=1 sin 90 0 n sinc=1 n=

36 3.Write the ray diagram showing the experimental arrangement for pure spectrum. S R L 1 V L 2 P

37 4.What is an optical fibre? on what principle does it work? An optical fibre is a thin transparent fibre which transmits light along any desired path. It works on the princple of TIR. 5.What is a pure spectrum? give an example. If the constituent colours are seen distinctly in a spectrum, it is called pure spectrum. Example: Spectrum produced in the laboratory 6.What is an impure spectrum? give an example. A spectrum in which the constituent colours overlap and are not seen distinctly is called impure spectrum. Example: Rainbow

38 7.Calculate the refractive index of a pair of media given critical angle as 40. given C=40,n=1 8.Calculate the angle of deviation produced by a thin prism of refracting angle5 and refractive index 1.5. d=?,a=5,n=1.5 d=(n-1)a =(1.5-1)X5 =0.5X5 =2.5

39 9.An object is kept at a distance of 0.12m from a convex lens forms an image at a distance of 0.18m.calculate the magnification produced. u=0.12m,v=0.18m, m=?

40 10.Two thin convex lenses of focal lengths 0.15m & 0.2m are separated by a distance of 0.6m. Find the effective focal length of the combination. given:f 1 =0.15,f 2 =0.2,d=0.06,F=?

41 Question carrying FIVE mark each 1. What is lateral shift? Derive an expression for lateral shift produced by a parallel sided glass slab for oblique incidence. 2. What is normal shift? Derive the expression for normal shift produced when an object in a denser medium is viewed normally through air. 3. Derive the expression for refractive index in terms of the angle of the prism and angle of minimum deviation.

42 4.Derive the relation connecting n,u,v & R for refraction at a spherical surface concave towards a point object in a denser medium. 5.Derive lens maker s formula. 6.Derive the expression for the effective focal length of two thin lenses in contact.

43 Read the given problem twice Write the given data Write a relevant formula/e connecting the given data Substitute and simplify Write the result with S.I unit

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53 March 2010 : Find the real position of an air bubble in a glass cube of side 0.3 m if the bubble appears to be at a distance of 0.05 m from one face and at 0.15 m from the opposite face. Solution: Here apparent distance from both the faces are given. A.D 1 A.D 2 = 0.05 m = 0.15 m Let x be the real distance from the first face. Real distance from the opposite face is (0.3-x) m

54 We know that Therefore the real position of the air bubble in the glass cube is 0.1 m from the first face or 0.2 m from the opposite face.

55 March 2008: Focal length of convex lens is 0.1 m. A liquid lens is formed between a plane surface and one face of this lens of radius of curvature 0.12m. The converging combination formed is found to have a focal length 0.18 m. Calculate the refractive index of liquid. Solution: Given F=0.18 m, f 1 = 0.1m, R 1 =0.12m, n=?

56 Here radius of curvature of the plane surface is infinity

57 March 2011: A concave lens when placed in air has a focal length of 0.4 m and has a refractive index of 3/2. What will be its focal length when immersed in water of refractive index 4/3. Solution: Given: f=0.4 m, n of glass=3/2, f of lens when immersed in water=? R.I of water 4/3

58 Simplify and arrive at

59 March 2006: A small air bubble is found 0.04 m inside the glass sphere of refractive index 1.5 When viewed normally from outside it is seen at a depth of 0.03 m. Calculate the radius of curvature of the glass sphere. Solution: Given u=0.04m, n=1.5, v=0.03m, R?

60 R=0.119m