Tiêu đề 24.Optics.pdf ✅

NEET-2022 Ultimate Crash Course PHYSICS RAY OPTICS AND OPTICAL INSTRUMENTS

POINTS TO REMEMBER 1. The mirror equation, i.e., 1 1 1 f u = +  is independent of the particular angle,  of the incident ray. In fact, it is applicable to all incident rays that make small angles with the principal axis. All such rays, called paraxial rays, converge (or appear to diverge from) the image point I. 2. For a distant point O, we can set u equal to  . In that case, the image is at the focal point (u f ) = and the equation 2 1 1 R u = +  gives 2 1 1 R f = +  or f = R/2, a result which we have already obtained independently in art. 12.3 3. If we interchange u and v in the mirror equation, the equation is unchanged. This implies the principle of optical reversibility, since interchanging u and v in this equation corresponds to physically interchanging the object and the image. 4. For a plane mirror, the radius of curvature, R = , From eqn. 2 1 1 1 1 , 0 or u, R u u = + + =  = −   i.e., the image lies as far behind the plane mirror as the objects is in front of it. 5. Magnification is negative for a real image and positive for a virtual image 6. In case of a convex mirror, image is always virtual (except when the object is virtual. Thus, m is positive 7. As 1 1 1 , u f u f    + = + =   (multiplying both sides by  ) Or 1 m f  − = (as m u  = − ) Or f m 1 f f  −  = − = Again u u u u f + =  (multiplying both sides by u) Or 1 u 1 / u f + =  Or 1 u 1 m f + = − Or 1 u 1 m f + = − as m u      = −   or 1 u 1 m f − = − or 1 u f u 1 m f f − = − = or f m f u = − clearly, I f f m O u f f u  −  = = − = = − ....................(5) 8. It can be easily shown that  = − f 1 m ( ) ..........................(6) and 1 u f 1 ................. m   = −     (7) 9. If g 3 2   = , then from eqn.(3) g a a g 1 2 3  = =  which is less than 1 10. From eqn. (5), 1 2 2 1   = 
Similarly , 2 3 3 1 3 1 2 3 and    =  =   Thus, 1 2 3 2 1 3 2 3 1 1 2 3 1         =   =    Also, 1 2 3 3 1 3 1 2 1 2 1   = =     For example, a w a a g g g w a w 3/ 2 9 3 4 as and 4/ 3 8 2 3     = = =  =  =      (here, g stands for glass, w for water and a for air) Alternatively, w g g w 9 8   = =  (using 1 2 2 1   =  ), where g w   and are the absolute refractive indices for glass and water relative to vacuum. Similarly, g w w g 4/ 3 8 3/ 2 9   = = =  which is less than 1. Thus, relative refractive index can be less than 1, but absolute (standard) refractive index is always greater than 1. 11. Refractive index of a medium, being a pure ratio, has no units and is a dimensionless quantity. Its value depends upon : (1) medium (2) wavelength of light employed (3) temperature and (4) the surrounding medium. 12. If i 1 2 > (i.e., μ2> 1 ), sin i> sin r or i > r or r < i, i.e., the refracted ray bends towards the normal as it travels from medium-1 to medium-2. Reverse is the case when 1  2 1 13. If 2 > 1 , medium-2 is optically denser than medium-1 and reverse is the case if 2 < 1 14. When light enters an optically denser medium, its speed decreases but instantaneously increases to its original value as it emerges out of the medium. For example, when a beam of light travelling in air enters glass, it may encounter an electron bound to an atom at A [Fig. 13.2]. Light is absorbed by the atom which causes the electron to oscillate. The oscillating electron radiates the beam of light towards an atom at B, where the light is again absorbed by an atom. Thus, light passes from one atom to another through the glass. Although light travels from one glass atom to another with a speed of 3 x 108 m/s, the absorption and radiation processes that take place in the glass, cause the speed to slow down. As soon as the light emerges out of glass, these slowing processes cease and it gains its original speed of 3 x 108 m/s. 15. It is interesting to note that Incident Reflected the law of reflection can be formally written in the same form as the law of refraction. The angles of incidence (i) and reflection (r) should be taken with opposite signs as we measure angles from the normal to the corresponding ray [Fig. 13.3]. Thus, the law of reflection should be written as i = — r or sin i 1 sin r = − Since in case of refraction, sin i , 1 sin r =   = − The law of reflection can thus be treated as a special case of the law of refraction for  = −1. 16. If the above analysis,  was regarded as a constant characteristic of medium which is not true for high intensity (I) radiation like the °lie of the laser beam. In such a case,