• # 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 $7000\,\overset{\text{o}}{\mathop{\text{A}}}\,$)