• # question_answer A glass plate 0.40 micron thick is illuminated by a beam of white light normal to the plate. The refractive index of glass is 1.50 and the limits of the visible spectrum are ${{\lambda }_{V}}=4000\ \overset{\text{o}}{\mathop{\text{A}}}\,$ and ${{\lambda }_{\operatorname{R}}}=7000\,\overset{\text{o}}{\mathop{\text{A}}}\,$. The wavelengths that get intensified in the reflected beam are A) $4800\,\overset{\text{o}}{\mathop{\text{A}}}\,$ and $5200\,\overset{\text{o}}{\mathop{\text{A}}}\,$ B) $4800\,\overset{\text{o}}{\mathop{\text{A}}}\,$and $6700\,\overset{\text{o}}{\mathop{\text{A}}}\,$ C)  only D) $5200\,\overset{\text{o}}{\mathop{\text{A}}}\,$ only

 for intensified reflected beam $2\mu t=(2n-1)\frac{\lambda }{2};n=1,2,...$ Or         $\lambda =\frac{4\mu t}{(2n-1)}=\frac{4\times 1.5\times 0.40\times {{10}^{-6}}}{(2n-1)}$ $=\frac{2.4\times {{10}^{-6}}}{(2n-1)}$ For $n=3,$ $\lambda =4800\,\overset{\text{o}}{\mathop{\text{A}}}\,$ (only wavelength between $4000\,\overset{\text{o}}{\mathop{\text{A}}}\,$ to $7000\,\overset{\text{o}}{\mathop{\text{A}}}\,$)
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.934789776802063, "perplexity": 709.7191817307986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304261.85/warc/CC-MAIN-20220123111431-20220123141431-00576.warc.gz"}