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Unit VI: Optics Chapter-9: Ray Optics and Optical Instruments GIST OF THE CHAPTER: Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lens maker’s formula, magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. CONTENT/ CONCEPTS- Reflection Reflection is the phenomenon of changing the path of light without any change in the medium. Reflection of Light The returning back of light in the same medium from which it has come after striking a surface is called reflection of light. Laws of Reflection Two laws of reflection are given as below: (i) The angle of incidence i is equal to the angle of reflectionr. ie. Zi= Zr. (ii) The incident ray, reflected ray and normal to the reflecting surface at the point of incidence all lie in the same plane. A SPHERICAL MIRROR: A spherical mirror whose reflecting surface is curved inwards, i.e. faces towards the centre of the mirror, is called a concave mirror A spherical mirror whose reflecting surface is curved outwards, i.e. faces away from the centre of the mirror, and is called a convex mirror. Pole (P) is the centre of reflecting surface lying on the surface. Centre of curvature (C) is the centre of the imaginary sphere from which spherical mirror is cut out. Radius of curvature (R) is the distance between the pole and the centre of curvature. Principal axis (PCX or CPX) is the line passing through the pole and the centre of curvature and extending to %. It is the normal to the mirror at the pole. Principal Focus (F) is the point on the principal axis at which the incident rays of light parallel to principal axis either really pass through or appear to pass through after getting reflected from the mirror. Focal len: is the distance between the pole and the principal focus. A MIRROR FORMULA 1 1 4 1 f vou u— Object distance v —Image distance f — Focal length of the mirror MAGNIFICATION PRODUCED BY A MIRROR Magnification produced by a mirror is defined as the ratio of the size of the image to the size of the object. Magnification produced by a mirror is also defined as the ratio of the image distance to object distance. h' v m=—>=-- h u SIGN CONVENTIONS FOR REFLECTION BY SPHERICAL MIRRORS 1, The object is always placed to the left of the mirror. i.e. the incident rays from the object always move from left to right. 2, All distances parallel to the principal axis are measured from the pole (P) of the mirror. 3. All the distances measured to the right of the Pole (along +ve x-axis) are taken +ve while those measured to the left of the Pole (along - ve x-axis) are taken —ve. 4. Distances measured perpendicular to and above the principal axis (along +ve y-axis) are taken +ve while those measured below the principal axis (along —ve y-axis) are taken —ve. sum of internal opposite angles, Therefore, in AIAC, r+B=y Pr=y-fP ----- (i) Similarly, in AOBC, i=at+y ---- (ii) According to Snell’s law, a . mn, simi agit (2) nm sinr or ( Angles are small) > r= ni Using (i) & (ii), we obtain > ni(y-B) = uy(at+y) As angle a, B, and y are small, using tan@ ~ @, we obtain {AM , AM \ (AM AM \ i nae + |= ny —— | (3) \MO MC} \MC MI ) As aperture of the spherical surface is small, M is close to P. Therefore using new Cartesian sign conventions MO = PO =-u, MI= Pl =+ v, MC= PC=R From (3), 1 1 1 1 nz My N2-Yy = m(e-d)em(S-8)= Bol PC PI PO PC PI PO PC Using new Cartesian sign conventions, we put Mg iy M2 => —+ v —u R (i) Refraction from rarer to denser medium Ng Ny Ng7-Mh im ay > m) vou R (ii) Refraction from denser to rarer medium Ny Ng Mm Nz SN (my > my) v u R Refraction by Spherical Lenses Lenses whose refracting surfaces are spherical are called ‘spherical lenses’. A spherical lens whose refracting surfaces are bulging outwards at the centre is called a ‘double convex lens’, It is thicker in the middle compared to the edges. A spherical lens whose refracting surfaces are curved inwards at the centre is called a ‘double concave lens’. It is thinner in the middle compared to the edges. LENS MAKER’S FORMULA (i) Refraction from rarer to denser medium Ng Mm Ng wy OU R, (nz > 1) (ii) Refraction from denser to rarer medium Ny Ng Ny — Ng Vv Vy Ry N (n, > nz) Adding two equations Taking v= f when u = co LENS FORMULA LINEAR MAGNIFICATION SIMPLE MICROSCOPE It is a convex lens of short focal length Eye focussed Magnifying power (m): The magnifying power of a ‘on near point microscope is defined as the ratio of the angle 6 subtended by the image at the eye to the angle @ subtended by the object seen directly, when both lie |——__D at the least distance of distinct vision. AY || COMPOUND MICROSCOPE Objective is a convex lens of short focal length and of small aperture . Eye piece is a convex lens ae of slightly larger focal Jength of larger aperture. a’ Magnification of the compound microscope (a) when the final image is formed at the least distance of distinct vision is given by, vy. = D L oD Vo (1 4. >) m=-—x—=m,m, = -— = o ve we Uo fe (b) Magnification of the compound microscope when the final image is formed at the infinity is given by, v, = 00 Vg (D momma 2 (7 o Ve 
