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OPTICS- 02-Theory-(26-38)

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(BRUSH UP YOUR CONCEPTS) 1. A transparent cylinder of radius R = 2.00 m has a mirrored surface on its right half as shown in figure. A light ray travelling in air is incident on the left side of the cylinder. The incident ray and exiting ray are parallel and at a distance 2.00 m. Determine the refractive index of the material. Incident ray 2m Exiting ray 2. A lens of a focal length of f = 30 cm produces on a screen a sharp image of object that is at a distance of a = 40 cm from the lens. A plane parallel plate with thickness of d = 9 cm is placed between the lens and the object perpendicular to the optical axis of the lens. Through what distance should the screen be shifted for the image of the object to remain distict ? (g = 1.8). 3. Surface of a thin equi-convex glass lens have radius of curvature R. Paraxial rays are incident on it. If the final image formed after n internal reflection, calculate distance of this image from pole of the lens. Refractive index of glass is . 4. When a plane surface of plano convex lens is silvered it is found that the image of object pin is formed at the position of the object pin placed at a distance of x1 from silvered lens. When same lens is silvered on the curved surface the image of the object pin is formed at the position of the object pin placed at a distance of x2 from the silvered lens. Find focal length of lens, the radius of curvature of curved surface and refractive index in term of x1 and x2. 5. The distance S between an object an its real image formed by converging lens, is held fixed. Show that there are two possible positions of the lens, and that the size of the object is given by (h1h2 ) 2 where h and h are the sizes of the two images. Show that h1 S s 2 where s is the separa- 1 2 h2 S s tion of the two positions. 6. Two thin convex lenses of focal length f1 and f2 are separated by horizontal distance d (where d < f1, d< f2) and their centers are displaced by a vertical separation x as shown in figure. Taking origin of coordinates O at the center of first lens find the x and y coordinates of focal point of this lens system, for a parallel beam of rays coming from the left. 7. Two converging lenses of the same focal length f are separated by distance 2f. The axis of second lens is inclined at angle = 60º w.r.t. the axis of the first lens. A parallel paraxial beam of light incident from side of the lens. Find the coordinates of the final image with respect to origin of the first lens. x 8. The refracting angle of prism is 60º, A ray of light passing through the prism undergoes a deviation of 40º. If the prism is rotated through an angle of 11º the same deviation is again obtained. Find refractive index of prism. 9. In the young’s double slit experiment distance between the slits is 1 mm. Screen is kept 1 m away from the slit when the light-wave of wavelength 4.0 × 103 Å falls on the slit interference pattern is observed on the screen. (a)

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- SUBJECTIVE UNSOLVED LEVEL - II (BRUSH UP YOUR CONCEPTS) 2m Incident ray Exiting ray 2m Incident ray Exiting ray 1. A transparent cylinder of radius R = 2.00 m has a mirrored surface on its right half as shown in figure. A light ray travelling in air is incident on the left side of the cylinder. The incident ray and exiting ray are parallel and at a distance 2.00 m. Determine the refractive index of the material. 2. A lens of a focal length of f = 30 cm produces on a screen a sharp image of object that is at a distance of a = 40 cm from the lens. A plane parallel plate with thickness of d = 9 cm is placed between the lens and the object perpendicular to the optical axis of the lens. Through what distance should the screen be shifted for the image of the object to remain distict ? (g = 1.8). 3. Surface of a thin equi-convex glass lens have radius of curvature R. Paraxial rays are incident on it. If the final image formed after n internal reflection, calculate distance of this image from pole of the lens. Refractive index of glass is . 4. When a plane surface of plano convex lens is silvered it is found that the image of object pin is formed at the position of the object pin placed at a distance of x1 from silvered lens. When same lens is silvered on the curved surface the image of the object pin is formed at the position of the object pin placed at a distance of x2 from the silvered lens. Find focal length of lens, the radius of curvature of curved surface and refractive index in term of x1 and x2 . 5. The distance S between an object an its real image formed by converging lens, is held fixed. Show that there are two possible positions of the lens, and that the size of the object is given by 1 2 1 2 ( ) h h where 1 h and 2 h are the sizes of the two images. Show that 2 1 2 S s h h S s where s is the separa- tion of the two positions. d x y O 6. Two thin convex lenses of focal length f1 and f2 are separated by horizontal distance d (where d < f1 , d< f2 ) and their centers are displaced by a vertical separation as shown in figure. Taking origin of coordinates O at the center of first lens find the x and y coordinates of focal point of this lens system, for a parallel beam of rays coming from the left.
- 7. Two converging lenses of the same focal length f are separated by distance 2f. The axis of second lens is inclined at angle = 60º w.r.t. the axis of the first lens. A parallel paraxial beam of light incident from side of the lens. Find the coordinates of the final image with respect to origin of the first lens. 2f x y 60º 2f x y 60º 8. The refracting angle of prism is 60º, A ray of light passing through the prism undergoes a deviation of 40º. If the prism is rotated through an angle of 11º the same deviation is again obtained. Find refractive index of prism. 9. In the young’s double slit experiment distance between the slits is 1 mm. Screen is kept 1 m away from the slit when the light-wave of wavelength 4.0 × 103 Å falls on the slit interference pattern is observed on the screen. (a) Find the distance of points from the center of screen where the intensity will be half of intensity at the center of screen. (b) Point where the intensity is zero. (c) If the length of the screen is 20 mm then find total maxima formed on the screen. (d) If the screen is sufficient long instead of 20 mm, then find the no. of maxima form on the screen. (e) If the screen substends 60º angle at the midpoint of the slit find total no of maxima formed on the screen. C S1 S2 Screen P C S1 S2 Screen P 10. A parallel beam strikes the sources at angle with the normal to the slits (a) For what value of at the center of the screen minimum is formed (screen is kept symmetrically to the slits) (b) Find intensity at a point P on the screen. [Point P makes angle with the screen]
- SUBJECTIVE UNSOLVED LEVEL - III (CHECK YOUR SKILLS) O r l a O r l a 1. A cubical block of glass 2 has a concentric spherical cavity of radius r = 3 cm. Each edge of the cube is l = 12 cm long. A luminous point object is at distance a = 12 cm on left of left face of the cube as shown in figure. Find apparent position of the object when seen from right side of the cube. 1=1.5 2=1 3=1.5 45cm 24cm 54cm O 20cm 4 3 10cm 4 3 1=1.5 2=1 3=1.5 45cm 24cm 54cm O 20cm 4 3 10cm 4 3 2. A composite slab consisting of different media is placed in front of a concave mirror of radius of curvature 150 cm. The whole arrangement is placed in water 4 3 . An object O placed at a distance 20 cm from the slab. Find the position of final image formed by the system. 3. Radius of curvature of surfaces of a bi-convex lens are R1 and R2 . Refractive index of lens material is n. Refractive index of medium on left of lens is n1 while that of medium on right of lens is n2 (a) Parallel light ray incident on lens from left, find distance f2 of point of convergence of refracted rays from optical center of lens. (b) If parallel rays are incident on lens from right, find distance f1 of point of convergence of refracted rays from optical center of the lens. (c) If an object is placed on left at a distance a from lens and its real image in formed at a distance b from lens. Find 1 2 f f a b 4. The convex surface of a thin concave-convex lens of glass of 3 2 has a radius of curvature 20 cm. The concave surface has a radius of curvature 60 cm. The convex side is silvered and placed on horizontal surface. At what distance from the lens should a point object be placed on the axis so that it coincides with its image ? If water is now filled 4 3 in the concave surface of the lens through what distance should the objected be shifted from its position in order to again coincide with its image. 5. One side of radius of curvature r1 = 120 cm of a convex lens of material of refractive index = 1.5 and focal length f1 = 20 cm is silvered. It is placed on a hz surface with silvered surface in contact with it. Another convex lens of focal length f2 = 20 cm is fixed coaxially d = 10 cm above. A luminous point object O on the axis gives rise to an image coincide with it. Find its height above the upper lens.
- A B C 45º 45cm A B C 45º 45cm 6. A 16 cm long pencil is placed at 45º angle with its centre 15.0 cm above the optic axis and 45.0 cm from a convex lens of focal length 20 cm as shown in figure. Assume that the diameter of lens is large enough for the paraxial approx to be valid (a) Where is the image of the pencil formed (give the location of the images of the points A, B and C) (b) What is the length of the image (the distance between the images of point A and B) 7. Three right angled prism of refractive index 1 2 , and 3 are joined together so that the faces of the middle prism are in contact each with one of the outside prisms. If ray passes through composite block undeviated shown that 2 2 2 1 3 2 1 . 5cm S 0.1cm 5cm 5cm S 0.1cm 5cm 8. In a Lloyd’s mirror of length 5 cm is illuminated with monochromatic light of wavelength 5460Å, from a narrow slip 0.1 cm from its plane 5 cm measured in the plane from near edge. Find (a) The separation of consecutive similar fringes at a distance of 120 cm from slit. (b) The total width the pattern observed. S1 Screen S2 S 45º 1 mm 2 2 m S1 Screen S2 S 45º 1 mm 2 2 m 9. Two slits 1 S and 2 S are on a plane inclined at an angle of 45º with horizontal. The distance between slits is 2 mm. a mono- chromatic point source S of wavelength 3 5 10 Å placed at a distance 1 2 mm from the midpoint of slits as shown in figure. The screen is placed at a distance m. Find the fringe width of interference pattern on the screen. D S1 S2 t1 t2 10. A screen is at distance D = 80 cm from diaphragm having two narrow slits 1 S and 2 S which are d = 2 mm apart. Slit is covered by a transparent sheet of thickness and by another sheet of thickness as shown in figure. Both sheet are made of same material having R.I = 1.4. Water is filled in space between diaphragmand screen. A monochromatic light beam of wavelength Å is incident normally on the diaphragm. Assuming intensity of beam to be uniform and slits of equal width, find ratio of intensity at C to max intensity of interference pattern obtained on the screen C is the foot of perpendicular to bisector of 1 2 4 3 S S .

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