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. stream 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 . <> ������A�]�j����~c�Wb�_��{�?�D��拕D�����N��naK�=���N�N[ ]�o���qA\$wgg�G���l�s��Q^ܿC܉�|�ol�F.? The following assumptions are taken for the derivation of lens maker formula. 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��� That is, x 1 = (p-f) and x 2 = (q-f) or q = f + x 2. 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. stream 4 measurements of the focal distances for the sphere and the hemisphere of the same radius. �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�� ?4W��o��^�:��!�W��ڛ�[��������h����=.��ܴW�x��w�]�5Yp�/. A lens will be converging with positive focal length, and diverging if the focal length is negative. Assumptions made: The lens is thin. 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 Lensmaker’s Formula by C. Bond Lenses with the same shape and index of refraction will have the same focal length. 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. That is, x 1 = (p-f) and x 2 = (q-f) or q = f + x 2. 12. 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 . EXAMPLE 7.1: lens in air and water . Examples are attached. 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 . So we can conclude that a convex lens need not necessarily be a converging and a concave lens diverging. Here, x 1 and x 2 are the distances to the object and image respectively from the focal points. 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. %PDF-1.3 the Thin Lens Equation: Sign conventions . 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. Learn lens makers formula. 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 . 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. The object lies close to principal axis. We can rewrite the Lensmaker’s formula in a form of . Place the lit candle near the flask. x��]ے�Ƒ}���#!��u/��^��GX �~����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. 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. We take the limit of \(t→0\) to obtain the formula for a thin lens. Tags: Class 10 , Physics , Light Reflection Refraction Asked by Rah 1 Answers. 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. 2 0 obj ���l[:msNC4<4��FR����E!�� �hi/��+��}��@�|sg5�(�ܐ�h,�o��ދ8�к] J&�6S�>�� ��JG�'e�m�T���ha�k�42�� =J\���a��T3�FE�K>}�n(���y�N.Ӗ6��f�;Z���8#1�(b�n�b��yv��x&B)̈́�����O�9�ȉNNg6y.x��o� ���+�+��c�'�{�рC�� 9;��,�~Ej���-F�S�ϧ�L�h�/�^Z�cܣ4����P����� �)5v���[���-N�3���~w���lw96��AI�^k:J��87a�Gv��,:+��J�@,8�(c��,o}ä��^ 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 Derivation for lens makers formula . is obviously not a thin lens and thus one wouldn’t expect the thin-lens formula to be totally correct. Lens Maker Formula Derivation. 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 . 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. 5 0 obj the Thin Lens Equation: Sign conventions . Here, x 1 and x 2 are the distances to the object and image respectively from the focal points. Assumptions. 12. (a) Fill the Florence flask with water and place it in the cork support ring on the lab bench. 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. Examples are attached. 4. 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{� A lens is said to be thin if the gap between the two surfaces is very small. the lensmaker’s formula relates the index of refraction, the radii of curvature of the two surfaces of the lens, and the focal length of the lens.