# thin film interference problems and solutions pdf

Thin Film Interference 12 n1 n2 n3 n1 endobj H�tT�n�0��+�HC�e h4MP�hQ��-Ɂ�i��-"#?����!� ��%9ܝ�Y��۽��I���m3�n�π�/D ��a5����6Iq���.qQ^@{Jȭ1��i�b���r/Fw�ƕ. A thin film of soap solution is illuminated by white light at an angle of incidence i = sin-1(4/5). 0000049847 00000 n Calculate the thickness of the film. 0000002200 00000 n %%EOF In addition to the path length difference, there can be a phase change. 0000003368 00000 n Antireflection coating with a TiO 2 thin film. xڭ]K�7���W}�#,ޏ����Ê��c�w}ѥ�����$��"����I_U@�ڣ {��#���� ��+�� 0000010136 00000 n stream (�5�P|�+����9)_�)�Y�����m���dQB)f������Aw(,gʝK��Ei �a�6��6�M�i6���@N�R9����m;l�~5T����2UD$�2�Z��A�P%i��E ix�כ:�S�"!&��BS��)=� rv�Va����n�H��k_�*8x�4՘R:�"�C2�t����n�\KiUk��r�]���.�: Thin film interference occurs between the light reflected from the top and bottom surfaces of a film. The refractive index for soap solution is 4/3. In the reflected light, two dark consecutive overlapping fringes are observed corresponding to wavelengths 6.1 x 10-7 m and 6.0 x 10-7m. 0000008342 00000 n 0000004800 00000 n 0 0000001352 00000 n P33-16 Thin Film: Extra Path d Extra path length ~ 2d ()1 2 When light hits a material that has multiple layers, each layer can reflect light. 0000006245 00000 n Reflections take place at the bottom of slab B and at the top of slab A. Thin Film Interference - Iridescence Image courtesy of John M. Sullivan, University of Illinois and Technical University of Berlin. In addition to the path length difference, there can be a phase change. << /Length 1 0 R /Filter /FlateDecode >> This film is really much thinner than either slab. 0000001272 00000 n 0000006507 00000 n 0000008921 00000 n Thin film interference occurs between the light reflected from the top and bottom surfaces of a film. The light reflected from any one 0000005167 00000 n 0000072630 00000 n startxref %PDF-1.4 %���� 0000003123 00000 n endstream endobj 33 0 obj<> endobj 35 0 obj<> endobj 36 0 obj<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 37 0 obj<> endobj 38 0 obj<> endobj 39 0 obj<> endobj 40 0 obj<> endobj 41 0 obj<> endobj 42 0 obj<> endobj 43 0 obj<>stream 0000001670 00000 n Thin film of oil. 1. Given, µ = 4/3, λ1 = 6.1 x 10-7 m λ2 = 6.0 x 10-7m solution: Sin i = 4/5 µ = Sin i / Sin r Sin r = sin i / µ = ⅘ / 4/3 = sin r = ⅗ = 0.6 cos r = √1 – sin2r = 0.8 Given two consecutive fringes are overlapping, nλ1 = (n + 1)… xref v��t��tC�]w��vV�$��0C���$Lk�|��)���S�����_�g:̗E�ӣ�U�ʢ���nTm�E%�r��P�K-%�P��&]"آ ����n��bæ� �^�_��mP6H �@���;�κ����!/��jS}pCI�7�� 2 0 obj 欓V+�nh��ހ��AD�Y��i�V���:��,��8#N&��g1�ͤ�S�(����yZl��\A�� �(� ��9LJJ@���jDG�m@ ������X ,�� �0�!���s�L������~0$0�e�e�����I���i9�"�������3<31cx�0��7�N.oN��s�A� bk� �8� 0000058704 00000 n Anti-reflection coating. %��������� P33-15 Thin Film Interference - Iridescence •Bubbles •Butterfly Wings •Oil on Puddles. E�*�1���Dt�����t���_��n�u)T U 9"�g���F ˼{42]�K�XT�yϜ0��m%gK����[��"0r� i� Thin film of water. 0000007629 00000 n 0000058475 00000 n 0000003444 00000 n Interference of direct and reflected light from a point source. 0000007080 00000 n �W6��o7M�����0g�;_�r{�D�0@ެ����m�n�i�� ]���b�3J�Q!��N�nQz����G������. 0000058968 00000 n 0000004545 00000 n x�bf�ae�� Ȁ �@16�[ 32 33 0000004415 00000 n Thin-film interference with white light. 0000005871 00000 n trailer PHY 2049: Chapter 36 14 Reflection and Interference from Thin Films ÎNormal-incidence light strikes surface covered by a thin film Some rays reflect from film surface Some rays reflect from substrate surface (distance d further) ÎPath length difference = 2d causes interference From full constructive to full destructive, depending on λ d n 1 n 2 n 0 = 1 �Kzs�$ f����B9j�S1����o�>|�G`rfyS(�S\ p7��Hd\b ��Lـ }x����F�&� �)-��6ɛ_���Ǜ�����\$��Q����D�9���Xc���:����|������/7������z������>ް����KR�>Q�Ln�ZЭ���Ն�ޭ��?Pڬ��vM�d'rZ�����%o>Im� Soap film with nonnormal incidence. 0000000016 00000 n 0000000956 00000 n 0000009531 00000 n O���꼢��FW�o��� ������VĿ०wK��7D���95BS��͒���8����F�5����>�3Υ Title: PROBLEM 2 – 20 points Author: Andrew Duffy Created Date: 4/4/2009 10:32:23 AM 0000001531 00000 n 34 0 obj<>stream Since the angle of incidence is practically zero for both reflecting surfaces the condition for a bright fringe is that 2nd = (m + 1 2)λ. When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a $$180^{\circ}$$ phase change (or a $$\lambda /2$$ shift) occurs. 0000002721 00000 n <<71f7b7fd265e8a4f803a19a221e7a725>]>> 0000004133 00000 n 0000002860 00000 n Antireflection coating of a lens. Reflection from a thin glass sheet.

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