Q118 / 120 · VITEEE 2007 · Physics

Following diffraction pattern was obtained using a diffraction grating using two different wavelengths $\lambda_{1}$ and $\lambda_{2} .$ With the help of the figure identify which is the longer wavelength and their ratios. Figure

  • A
    $\lambda_{2}$ is longer than $\lambda_{1}$ and the ratio of the longer to the shorter wavelength is $1.5$
  • B
    $\lambda_{1}$ is longer than $\lambda_{2}$ and the ratio of the longer to the shorter wavelength is $1.5$
  • Correct answer
    C
    $\lambda_{1}$ and $\lambda_{2}$ are equal and their ratio is $1.0$
  • D
    $\lambda_{2}$ is longer than $\lambda_{1}$ and the ratio of the longer to the shorter wavelength is $2.5$.

Solution

Since position of central maximum is same, hence $\operatorname{asin} \theta=\lambda$ is same for both wavelengths. i.e, $a=$ constant, $\theta=$ same, $\Rightarrow \lambda$ is same for both waves $\Rightarrow \lambda_{1}=\lambda_{2}$ and $\frac{\lambda_{1}}{\lambda_{2}}=1$

Hence, the correct answer is option: 'C'.

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