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Class XII Mathematics Mathematics Part-II 7 ® P (E ∩ F) = P (F) P (E|F), P (F) ≠ 0 ® If E and F are independent, then P (E ∩ F) = P (E) P (F) P (E|F) = P (E), P (F) ≠ 0 P (F|E) = P (F), P(E) ...
Class XII Mathematics Mathematics Part-II 7 of probability lies in the correspondence between two great men of the seventeenth century, Pascal (1623-1662) and Pierre de Fermat (1601-1665). A ...
Class XII Physics Physics Part-II 1 Chapter Nine RAY OPTICS AND OPTICAL INSTRUMENTS 9.1 I NTRODUCTION Nature has endowed the human eye (retina) with the sensitivity to detect electrom...
Class XII Physics Physics Part-II 1 reflecting and refracting surfaces. We then go on to describe the construction and working of some important optical instruments, including the hum...
Class XII Physics Physics Part-II 1 follow the Cartesian sign convention. According to this convention, all distances are measured fromthepoleofthemirrorortheoptical centre of the len...
Class XII Physics Physics Part-II 1 the mirror. The geometry of reflection of an incident ray is shown in Fig. 9.4. Let C be the centre of curvature of the mirror. Consider a ray para...
Class XII Physics Physics Part-II 1 (i) The ray from the point which is parallel to the principal axis. The reflected ray goes through the focus of the mirror. (ii) The ray passing th...
Class XII Physics Physics Part-II 1 get B′F B′P –FP B′P FP = FP = BP (9.6) Equation (9.6) is a relation involving magnitude of distances. We now apply the sign convention. We note tha...
Class XII Physics Physics Part-II 1 by a concave and convex mirror. You should verify that Eqs. (9.7) and (9.9) are valid for these cases as well. FIGURE 9.6 Image formation by (a) a ...
Class XII Physics Physics Part-II 1 of a concave mirror of radius of curvature 15 cm. Find the position, nature, and magnification of the image in each case. Solution The focal length...
Class XII Physics Physics Part-II 1 (for u = –39 + 5 = –34) is (34/35 )m. 4 Reprint 2026-27 Physics The shift in the position of image in 1 s is 39 − 34 = 1365 −360 = 5 = 1 m 40 35 14...
Class XII Physics Physics Part-II 1 is constant. Remember that the angles of incidence (i) and refraction (r ) are the angles that the incident and its refracted ray make with the nor...
Class XII Physics Physics Part-II 1 index of medium 3 with respect to medium 2 then n 32= n × n , where n is the refractive index of 31 12 31 medium 3 with respect to medium 1. Some e...
Class XII Physics Physics Part-II 2 Wave Optics Chapter Ten WAVE OPTICS 10.1 I NTRODUCTION In 1637 Descartes gave the corpuscular model of light and derived Snell’s law.Itexplainedthe...
Class XII Physics Physics Part-II 1 If the angle of incidence isincreasedstillfurther(e.g.,therayAO ),4 refractionisnotpossible,andtheincident ray is totally reflected. This is called...
Class XII Physics Physics Part-II 1 few drops of milk or any other suspension to water and stir so that water becomes a little turbid. Take a laser pointer and shine its beam through ...
Class XII Physics Physics Part-II 1 material of the prism must be less than 45°. We see from Table 9.1 that this is true for both FIGURE 9.12 Observing total internal crown glass and ...
Class XII Physics Physics Part-II 1 used as a ‘light pipe’ to facilitate visual examination of internal organs like esophagus, stomach and intestines. You might have seen a commonly a...
Class XII Physics Physics Part-II 1 1 f1 L 1 1 1 P v − −30 10 A 1 X or v1= 15 cm 238 E Reprint 2026-27 Ray Optics and Optical Instruments The image formed by the first lens serves as ...
Class XII Physics Physics Part-II 1 which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, we sh...
Class XII Physics Physics Part-II 1 Equation (9.16) gives us a relation between object and image distance in terms of refractive index of the medium and the radius of curvature of the...
Class XII Physics Physics Part-II 1 DC 2  Suppose the object is at infinity, i.e., OB and DI = f, Eq. (9.19) gives n1  1 1  = (n2−n )1  +  (9.20) f BC 1 DC 2  The point where i...
Class XII Physics Physics Part-II 1 for a real image formed by a convex lens, the formula is valid for both convex as well as concave lenses and for both real and virtual images. It i...
Class XII Physics Physics Part-II 1 all cases. Here again it must be remembered that each point on an object gives out infinite number of rays. All these rays will pass through the sa...
Class XII Physics Physics Part-II 1 angle by which it converges or diverges a beam of light parallel to the principal axis falling at unit distance from the optical centre (Fig. 9.18)...