The lens equation tells us everything we need to know about the image of an object that is a known distance from the plane of a thin lens of known focal length. �g����.�c��i�N�����Wz����R��+����d�H6E2ʆ���釷�H�����iK�j�B[o�*�2�$W��UTg�����:j�� � �I�@4 ��>���D�Ԇ)�Ly+�M�ޓpA(lni4g�2Ô�6^:�m��-�6L�� Here, x 1 and x 2 are the distances to the object and image respectively from the focal points. For an ordinary thin lens in air: ' 1 and , we arive at the usual thin lens equations:n n rvsw== = = 2/20/2009 Matrix Methods in Paraxial Optics 6 21 o 11 1 and and s i io s mfff sf s += =− = =− The matrix methods in paraxial optics For optical systems with many elements we use a systematic approach called matrix method. << /Length 4 0 R /Filter /FlateDecode >> Assumptions made: The lens is thin. �~����ʑȟL!�ʑ�wN����Q´����G�/�-=&p�瘮��+�����B���[�7������ ocbᗘP��D?/���{���|-F'9mw3�2�DN'�� Kq����[$�S�x��9j��c��a�X:�o1�a' Xpy����W�ǐ���:��gEAICz�f��h���m�JL���床 �r�Q�J� G~n���;�*1� �fT�C;��A�-n��k1�ܽ�w�j�n��af��~�쵃�H�m���l��W�����I�4,ϥ9���`,�u���t��sI8v��l�GϚ�W����,B�� t��Oi����T 5�r�����4M�&RK��W5�4`ҽ+�x�>�܀����ƫ�깙R�¹�H� �'7u(�������aM伹���2Ŝ���i�2��L��i���cf̻i-�+T�kX���?R���r/YA�M��3�#��������N�t���\�U����'�=x��#��b�G��x�T��Y6E������xA����w�w�o&��0J��`�t�����\���nq�uB�v���Z-�?�1UU��C�����H�~������|����9����sv��VH72~?�"�u_c. The lens has a small aperture. Place the lit candle near the flask. A lens will be converging with positive focal length, and diverging if the focal length is negative. Lens Maker Formula Derivation. The following assumptions are taken for the derivation of lens maker formula. approximations that led to the “thin lens formula”, and requires a few additional parameters to describe it Front and Back focal lengths Primary and secondary Principle planes . 12. Numerical Methods In Lens (A) Lens Formula Definition: The equation relating the object distance (u), the image distance (v) and the focal length (f) of the lens is called the lens formula. The object lies close to principal axis. A lens is said to be thin if the gap between the two surfaces is very small. thin lens curved curved interface interface O O O n R n n R n ª ºª º »« » ¬ ¼¬ ¼. Lecture Notes on Geometrical Optics (02/18/14) 2.71/2.710 Introduction to Optics –Nick Fang . <> That is, x 1 = (p-f) and x 2 = (q-f) or q = f + x 2. So we can conclude that a convex lens need not necessarily be a converging and a concave lens diverging. (a) Fill the Florence flask with water and place it in the cork support ring on the lab bench. %��������� the Thin Lens Equation: Sign conventions . If light is incident from the left (as will be considered in most of the questions and sketches) the signs of spherical surfaces are as follows: A convex lens (left) has a positive focal length, a concave lens (right) has a negative focal length . SF017 SF027 51 1.5 Thin Lenses Formula and Lens maker’s Equation {Considering the ray diagram of refraction for 2 spherical surfaces as shown in figure below. %PDF-1.3 Learn lens makers formula. We can rewrite the Lensmaker’s formula in a form of . x��YKs7�ϯ��L�*����!�REU�Vq09���M��`b�;���hF�y�7�]��jZ����5����Z������ᥫ�~�n+� @m}��UeT�…��2���41����U}]���zةGiAغ�~�6 ��7�o�kDP��� 2 0 obj 5 0 obj Terms used with Thick Lenses 4 Focal lengths are measured from the vertex of the lens (not the center) and are labeled as the front focal length and the back focal length. (f is negative for a diverging lens). An alternate lens formula is known as the Newtonian Lens Formula which can be easily verified by substituting p = f + x 1 and q = f + x 2 into the Gaussian Lens Formula. EXAMPLE 7.1: lens in air and water . k�0���=�CA���R§�ۍ���C0�Y�j��!-H�I��E`�p��n�6Bz����)�޾����]�Q��`���tB+���JK\\"�5!K��ӊ48 An alternate lens formula is known as the Newtonian Lens Formula which can be easily verified by substituting p = f + x 1 and q = f + x 2 into the Gaussian Lens Formula. stream x��]ے�Ƒ}���#!��u/��^��GX Again, measure the object distance and the image distance from the center of the lens. To derive the thin-lens equation, we consider the image formed by the first refracting surface (i.e., left surface) and then use this image as the object for the second refracting surface. 3��~�+���{4���/��L���[��+=�݅BV^N����������Mv�'t�����.V�����{k���M�?ݪ�����z���ߧ��l�|��c�����ˮ�҅��ګ����u�����x���ퟨ�u�n�7�o�w�������k�͕���G�[\�}q��i�w���X�X_8f}��wX�nrI}��x�9w���n��|��p��b}u����d���M��>�4|����?K龥��2,-��6� ��y��yx~���?l����~�ݮ��3;�Cv����G��k���;�Ys�g}O~2�?� ?���9��?q���of���?� .�s���۸��͏/ȳayv,��oϛ����g��5b�_��i{� The incident rays make small angles with the lens surface or the principal axis. SF017 SF027 51 1.5 Thin Lenses Formula and Lens maker’s Equation {Considering the ray diagram of refraction for 2 spherical surfaces as shown in figure below. Derivation for lens makers formula . %�쏢 Examples are attached. The equation derived for a thin lens and relating two conjugated points is: (2) For the thick lens, so ... determine the formulae for the focal distance of the hemisphere and the sphere in terms of R and n. Once you have these equations, you should be able to find n from the . 4. stream O C 1 II C 2 1 P 1 P 2 I2 B E A D u1 v1 v2 r1 r2 t n1 t −v1 n2 n1 SF027 52 {By using the equation of spherical refracting surface, the refraction by first surface AB and second surface DE are given by is obviously not a thin lens and thus one wouldn’t expect the thin-lens formula to be totally correct. (f is negative for a diverging lens). The lens equation tells us everything we need to know about the image of an object that is a known distance from the plane of a thin lens of known focal length. Examples are attached. EXAMPLE 7.1: lens in air and water .