Department of Physics and Applied Mathematics Optics, Second Sessional May 09, 2022) Time: 1.5 br Max. Marks 25, gy 6 = ‘An air wedge is formed between two glass plates separated at one edge by a very fine wire, as shown in Figure. When the wedge is illuminated from above by 600-nm light and viewed from above, 30 dark fringes are | observed. Calculate the radius of the wire. ee ner ® yw oe Moving aceon Merference effects are produced at point P on a soreen as a result + of direct rays from_a 500-nm so reflected rays from the mitror, as shown in Figure. Assume the source is 100 m to the left of the screen and 1.00 cm above the mirror, Find the distance y to the first dark band above the mirror. v L Q3 : . S 4 ® Mirror MI in Figure is displaced a distance L. During this ht co displacement, 250 fringe reversals (formation of successive dark or a bright bands) are counted. ‘The light being used has a wavelength of 632.8 nm. Calculate the displacement, L. eo ow ws B® 8 - Ligne Monochromatic light from a helium-neon laser (A = 632.8 nm) is owe’ incident normally on a diffraction grating containing 6 000 grooves per centimeter. a) Find the angles at which the first- and second-order a, eur maxima are observed. 6) Wve fk forthe hod eso? Do we Sd in ner Ww drs = ot ® ee Sine = a BI When a gaseous element is raised to a very high temperature, the atoms emit radiation having discrete wavelengths. The set of wavelengths for a given element is called its atomic spectrum. Two strong components in the atomic spectrum of sodium have wavelengths of 589.00 nm and $89.59 nm. a) What resolving power must a grating have if these wavelengths are to be distinguished? b) To resolve these lines in the second-order spectrum, how many slits of the grating must be illuminated? a6 6 6 AA diffraction pattern is formed on a screen 120 cm away from a 0.400-mm-wide slit. Monochromatic 546.1- nm light is used. Calculate the fractional intensity I/max at a point on the screen 4.10 mm from the center of the principal maximum.rn” Qs. (05 points) ‘double-slit interference pattern is produced on a creen, as in Fig. 5; the light is monochromatic at a wavelength of 600 nm, A strip of transparent plastic | with index of refraction n= 1.50 is to be placed over Hl a feo Hl ada tinge one of the slits. Its presence changes the interference a " between light waves from the two slits, causing the interference pattern to be shifted across the screen from the original pattern. Figure 5 (a) shows the « © original locations of the central bright fringe (m = 0) and the first bright fringes (m = 1) above and below the central fringe. The purpose of the plastic is to shift the pattern upward so that the lower m =1 bright fringe is shifted to the center of the pattern. Should the plastic be placed over the top slit «+ (as arbitrarily drawn in Fig. 5 (b) or the bottom slit, and what thickness t should it have? & Ws bac 3 (06 points) \*AF 4 A Bu a) Fig (6-a) shows four long horizontal layers A-D of different materials, with air above and below them. The index of refraction of each material is given. Rays of light are sent into the left end of each layer as shown. In which layer is there the possibility of totally trapping the light in that layer so that, after many reflections, all the light reaches the right end of the ie Give brief reasoning to sly your answer. _ eet ne i. Fig (6-b), light travels from material w, through three layers of other materials with surfaces parallel to one another, and then back into another layer of material @. The refractions (but not the associated reflections) at the surfaces are shown. Rank the materials according to index of refraction, greatest first. Also give brief reasoning to satisfy your answer. nus (ye Q7. (16 points) ene bow ake! is the basic principle of laser? Can you get lasing from two level systems? If yes; how? If 0; why? ean lasing schemes (population of energy levels by pumping) in a two, three and four level it are the major types of fiber optic configuration that are used now days? Elaborate your swer by using diagrams. Also draw their index profile. aeBS Physics (Spring Semester 2022) PAM-270- Optics (Final Examination June 11, 2022) Maximum Time: 3hr Maximum Marks: 50 (05 points) A beam of un-polarized light of intensity To passes through a series of ideal De polarizing filters with their polarizing h directions turned to various angles as shown in Fig. (1) What is the light intensity (in terms of I,) at points A, B = and C (b) If we remove the middle filter, what will be the light intensity at point C? ve (06 points) a) Figure 2 shows a triangular prism of glass, a ray incident normal to ‘one face being totally reflected. If 0 is 45°, what is the refractive index of the glass? = —> |e) ‘What happens with the reflected ray if the prism (assuming nj= 1.5) is immersed in water (n2= 1.33)? Unpolarized ae SN ze ae Q3. (06 points) aA aA=\-33 ar Kephesical fish bowl has a diameter“of 30 cm. A small fish (small enough to be considered as a point object) is located ‘on axis 5 em to the right of the center of the fish bowl. An observer is looking into the fish bowl from the left. Where is the image of the fish that the observer will perceive as the true object? Give this location with respect to the front surface of the fish bowl. {__D>Now the observer put a lid on the fishbowl soit is sealed. ‘The observer jumps with the fish bowl into a large pool of water. The fish is lazy and has not moved from its original location in part (a). The front surface of the bowl is 30 em from the observer's eye. Where is the image of the fish that / the observer perceives as the true object? Give this location with respect to the front surface of the fish bowl. | se (06 points) tier lew ‘An observer to the right of the mirrorlens combination shown in ‘Object Figure 4 sees two real images that are the same size and in the same location. One image is upright and the other is inverted. Both images are 1.50 times larger than the object. The lens has a focal length of 10.0. cm. The lens and mirror are separated by 40.0 cm. Determine the focal length ofthe mirror. Do not assume that the figure is drawn to scale.Department of Physics and Applied Mathematics BS Physics (Summer Session 2022) PAM-270- Opties (First Sessional July 29, 2022) Maximum Time: 1.5 hr Maximum Marks: 25 A In Fig.1, un-polarized light is sent into a system of three polarizing sheets. The angles @1, @, and @; of the polarizing directions are measured counterclockwise from the positive direction of the y axis (they are not drawn to scale). Angles @ and @ are fixed, but angle 6 can be varied. Figure gives the intensity of the light emerging from sheet 3 as a function of @2. (The scale of the intensity axis is not percentage of the light’s initial intensity is transmitted by the system when 6 = 30°? a (05 points) In Fig2, light is incident at angle 4 = 40.1° on a boundary ‘between two transparent materials. Some of the light travels down through the next three layers of transparent materials, While some of it reflects upward and then escapes into the air. If ny =1.30, nz = 1.40, ms = 1.32, and ng = 1.45, what is the value of (a) Qs in the air and (b) Q: in the bottom material? - ee : (05 points) The thin glass shell shown in Fig. 3 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 em from the center of the mirror along the optic axis, as shown in the 3.30 mm figure. (a) Calculate the location and height of the image of this seed. (b) Suppose now that the shell is reversed. Find the location and height of the seed’s image. io vv Wane ae x 7 6) 4? Neare R we ral (05 points)DS Pysion PAN SERRE ~~ f$+-—- Opties (Second Sessional, May 15, 2023) ~ ‘Time: 1.5 hours Total Marks: 25 we 2 points versus angle 0 forthe noo diffetion patterns. IF both wavelengths are then used simultaneously, what color will be seen in the combined i pater at (a) angle A and (b) angle B? Lae 4 points tna doublesstit experiment, the wavelength of the light source is 405 nm. the slit separation is 19.4 mim, and the sit ‘wie is 4.080 mmm, Consider the interference ofthe ight from the two slits and also the diffraction of the light through each slit. (a) How many bright interference fringes are within the central peak of the diffaction envelope? (b) How many bright fFinges are within cither of the first side peaks of the diffraction envelope? ve 76 Be Sins A diffraction grating having 180 lines'mm is illuminated with a ral containing only two wavelengths, 2 = 400 fam and 2; = $00.am. The signal is incident perpendicularly on the grating. (a) What is the angular separation between ‘the second-order maxima of these two wavelengths? (b) What is the smallest angle at which two of the resulting maxis _are Superimposed? (c) What is the highest order for which maxing-for-boty wavelengths are present in the diffraction pattern? 4 points Plane-polarized light is incident on a single polarizing disk with the direction of Ey parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity inthe transmitted beam is reduced by 2 factor of (a) 3.00, (b) 5.00, c) 10.02 he S pints Light srikes 2 water surface atthe polarizing angle. The part ofthe bean Tr refracied into the water siikes a submerged glass slab (index oF refraction, 1.50), as shown in Fig. The light reMected rom the upper surface of the slab is completely polarized. Find the angle between the water surface and the glass stab (a6 5 points sheet is covered by a very th ing. In the mide of this shoot there is thin seratch 0.00125 me thick. The sheet is totally immersed ben surface of w liquid. Parallel rayseor monoelomatic coherent Hight witis wavelength 612 nm in air strike the sheet perpendicular to its surface and pas tl the Soratch. A screen is placed inthe fig a distance of 30.0 em aay fom the shot wd paral Wt, You sere tht fst dark fringes ome side of the central bright fringe on the ser ite 22.4 cn apart, What iy the retin ndes of the liquid “ ob ib anDepartment of Physics and Applied Mathematics Optics, First Sessional (April 11, 2022) ‘Time: 1.5 br we i /* shallow glass dish is 4.00 cm wide at the bottom, as shown Max. Marks 20 ~ in Figure. When an observer's own, the observer sees the edge of the botto |. When this dish is filled with water, the observer sees the-centre-of thie Bottom of the dish. Find the height of the dish. } T {s it possible to have total internal reflection for light incident from air on water? Explain. Calculate the critical angle for which TIR occur. You may take the refractive index of water 1.3337” ce ‘a Figure shows an overhead view of a corridor with a plane mirror Af mounted at one end. A burglar B sneaks along the corridor directly toward the center of the mirror. If d = 3.0 m, how far from the mirror will she be when the security guard Scan first see him in the mirror? a i) Figure shows a thin glass (n = 1.50) converging lens for which the radii of curvature are Ry = 15.0 cm and Re =-12.0.om. To the left of the lens is a cube having a face area of 100 cm”. The base of the cube is on the axis of the lens, and the right face is 20.0 cm to the left of the lens. (a) Determine the focal length of the lens. (b) Draw the image of the square face formed by the lens. What type of geometric figure is this? (¢) Determine the area of the image. ae 8) In Figure, assume that the two light waves, of wavelength 620 nm in air, are initially gut of phase by 7 rad. The indexes of Tefraction of the media are ny = 1.45 and np = 1.65, What are the (a) smallest and (b) second smallest valtic of L that will put the waves exactly in phase once they pass through the two media? “a A KaDepartment of Physics and Applied Mathematics Optics, First Sessional March 29, 2023 Time: 1.5 hr Max. Marks 25 val (6) For each thin lens shown in Fig, 1, calculate the location of the image of an object that is [/ \p~1o0en/ |p ~ 1a0em \fp = 1o0em | |p = 10cm 18.0 cm to the left of the lens, The lens material = 1500m {fra p~1s00m [fp 150em has a refractive index of 1.50, and the radii of ¢ shown are only the magnitudes. curvature shown are only ra te a e Z i An {5} + a polk Rays from a lens are converging toward a point image P located to the right of the lens. What thickness t of glass with index of refraction 1.60 must be interposed between the lens and P for the image to be formed at P’ located 0.30 em to the right of P? The locations of the piece of glass and of points are shown in Fig. 2. \ at wy x K Qs oe Se In Fig. 3. assume that the two light waves of wavelength = __p_—__"2__, 20nm inair, are initially out of phase by x rad, The indexes | —»>—______»— of refraction of the media are ni = 1.45 and np = 1.65. What 2 : is the smallest value of L that will put the waves exactly in we ws phase once they pass through the two media? art x Vos 1s , A spherical mirror is cut in half horizontally. Will an image be formed by the bottom half of the mirror? Iso, where will the image be formed? What will be the size of image? JOS (6) Viewing screen Interference effects are produced at point P on a screen because of direct rays from a 500-nm source and reflected rays from the mirror, as shown in Fig 5. Assume the source is 100 m to the left of the screen and 1,00 cm above the mirror. Find the distance y to the first dark band above the mirror. i at score” f\ (\ SAQs (05 points) A 16.0-cm-long pencil is placed at a 45° angle, with its center 15:0 cm above the optic axis and 45.0 cm froma lens with a 20.0-cm focal length as shown in Fig. Assume that the diameter of the lens is large enough for the paraxial approximation to be valid. (a) Where is the image of the pencil? (Give the location of the images of the points A, B, and C on the object, which are located at the eraser, point, and center of the pencil, respectively.) (b) What is the length of the image (that is, the distance between the images of points A and B)? (c) Show the orientation of the image in a sketch. a A method for measuring the index of refraction of glass is illustrated in Figure. One face of a slab of thickness 1 is painted white, and a small hole scraped clear at point P serves as a source of diverging rays when the slab is illuminated from below. Ray PBB/ F \. strikes the clear surface at the critical {zine angle and is totally reflected, as are rays such as PCC’. Rays such as PAA’ emerge from the clear surface. On the painted surface there appears a dark circle of diameter d, surrounded by an illuminated region, or halo. (a) Derive an equation for n in terms of the measured quantities ¢ and ¢. (b) What is the diameter of the dark circle if n = 1.52 for a slab 0.600 cm thick? (c) If white light is used, the critical angle depends on color caused by dispersion. Is the inner edge of the white halo tinged with red light or violet light? Explain.fas. ) mm (05 points) double-slit interference pattern is produced on a 7 sereen, as in Fig. 5; the light is monochromatic at a ] wavelength of 600 nm. A strip of transparent plastic i" '* a7) with index of refraction n = 1.50 is to be placed over Hl , Haze fl ge ‘one of the slits. Its presence changes the interference between light waves from the two slits, causing the interference pattern to be shifted across the screen from the original pattern. Figure 5 (a) shows the (24 tae original locations of the contral bright fringe (m = 0) and the first bright fringes‘(m = 1) above and below the central fringe. The purpose of the plastic is to shift the pattern upward so that the lower m =I bright fringe is shifted to the center of the pattem. Should the plastic be placed over the top slit (as arbitrarily drawn in Fig, 5 (b) o the bottom slit, and what thickness t should it have? (06 points) Fig (6-2) shows four long horizontal layers A-D of different as i 13 ‘materials, with air above and below them. The index of refraction of each material is given, Rays of light are sent into the left end of each 1sCB layer as shown. In which layer is there the possibility of totally ae trapping the light in that layer so that, after many reflections, all the 7s Tight reaches the right end of the layer? Give brief reasoning to satisfy your answer. k b, ae (7? lnFig. Fig 6), light travel fibm material a, through three layers of other materials with surfaces parallel to one another, and then back into another layer of material a. The refractions (but not the associated reflections) at the surfaces are shown. Rank the materials according to index of refraction, greatest first. Also give brief reasoning to satisfy your answer. Q7. (16 points) ‘49’ What isthe basic principle of laser? Can you get lasing from two level systems? IF yes: how? If “0; why? vy Draw lasing schemes (population of energy levels by pumping) in a two, three and four level system, ©) What are the major types of fiber optic configuration that are used now days? answer by using diagrams. Also draw their index profile, syns a=! a, met epg ye Elaborate yourHafser [amet] Department of Physics and Applied Mathematics Optics, First Sessional (April 11, 2022) Time: 1.5 hr (ye 4 Max. Marks 20 ~ E Gri ter PE x63) ig A shallow glass dish is 4.00 cm wide at the bottom, as shown 7 in Figure. When an observer's eye is place as shown, the eae observer sees the edge of the bottom of the eripty dish, When aan) this dish is filled with water, the observer sees the centre of the bottom of the dish. Find the height of the ish. Pets we TV pelntfe™ aw 8) Is it possible to have total internal reflection for light incident from air on water? Explain. Calculate the critical angle for which TIR occur. You may take the refractive index of water 1.3337 vise, OF pea Spy 4) Sheet Boo t figure shows an overhead view of a corridor with a plane mirror Af | mounted at one end. A burglar A sneaks none the comidordireetly (ward the Center of the mirror. If d = 3.0 m. how far from the mirror will she be when the security guard can first see him in the mirror? faseefor SIE yagi A: Figure shows a thin glass (n = 1.50) converging lens for which the radii of curvature are Ry = 15,0 em and Ry = 12.0 em. To the lelt of the lens is a cube having a face area of 100 cm*, The base of the cube is on the axis of the lens, and the right face is 20.0 em to the left of the lens. (a) Determine the focal length of the lens. (b) Draw the image of the square face formed by the lens. What type of ~» — geometric figure is this? (c) Determine the area of the image.” Qs BI In Figure, assume that the two light waves, of wavelength 620 ram in air, are initially out of phase by x rad. The indexes of refraction of the media are n, = 1.45 and n; = 1.65. What are the (a) smallest and (b) second smallest value of L that will put the waves exactly in phase once they pass through the two media?‘pues, Second Sessional May 09, 2022) Pare emer Time: 1.5 hr Max. Marks 25 as (s} An air wedge is formed between two glass plates separated at one edge -——sH——, by a very fine wire, as shown in Figure. When the wedge is illuminated from above by 600-nm light and viewed from above, 30 dark fringes are i = observed. Calculate the radius of the wi 15] Viewing sereen Interference effects are produced at point P on a sefesn as a 1st of direct rays from 9 50Q-nm sowpée arid reflected rays from the mirror, as shown in Figure. Assume the source is 100 m to the left of the screen and 1,00 cm above the mirror. Find the distance y to the first dark band above the mirror. 7 Mu) Mirror MI in Figure is displaced a distance L, During this es displacement, 250 fringe reversals (formation of successive dark or bright bands) are counted. The light being used has a wavelength of 632.8 nm, Calculate the displacement, L. Lend z£. By" i jonochromatic ight from a helium-neon laser (= 632.8 nm) is *"ree ’ incident normally on a diffraction grating containing 6 000 grooves per centimeter. a) Find the angles at which the first- and second-order maxima are observed. l taste b) What if we look for the third-order maximum? Do we find me it? as (31 ANvhen a gaseous element is raised to a very high temperature, the atoms emit radiation ing discrete ‘wavelengths. The set of wavelengths for a given clement is called its atomic spectrum, ‘Two strong components in the atomic specirun: of sodiutA ewe wavelencths of 589,00 nm and $89.59 nm. a) What resolving power must a grating have if these wavelengths are to be distinguished? b) To resolve these lines in the second-order spectrum, how many slits of the grating must be illuminated? 46.05 qe 6 = a dyind= a6 5) Qa A diffraction pattern is formed on a screen 120 cm away from a 0.400-mm-wide slit. Monochromatic 546.1- nm light is used, Calculate the fractional intensity Imax at a point on the sercen 4.10 mm from the center of the principal maximum. | + a "eo xb >(05 points)