Q123 / 180 · NEET 2019 (Odisha) · Physics

Angular width of the central maxima in the Fraunhoffer diffraction for $\lambda=6000 Å$ is $\theta_0$. When the same slit is illuminated by another monochromatic light, the angular width decreases by $30 \%$. The wavelength of this light is

  • A
    $1800 Å$
  • Correct answer
    B
    $4200 Å$
  • C
    $6000 Å$
  • D
    $420 Å$

Solution

The angular width of central maxima is given by $$ 2 \theta=\frac{2 \lambda}{\mathrm{a}} $$ where, $\lambda$ = wavelength of light used $\mathrm{a}=$ width of the slit For $\lambda_1=6000 Å, 2 \theta=\theta_0$ (given) For another light of wavelength $\lambda_2$ (says), the angular wid th decreases by $30 \%$ so, $$ 2 \theta=\left(\frac{100-30}{100}\right) \theta_0=\frac{70}{100} \theta_0=0.7 \theta_0 $$ As slit width is constant, so using Eq. (i) for these values, we get $$ \begin{gathered} \frac{\theta_0}{0.7 \theta_0}=\frac{\lambda_1}{\lambda_2} \\ \Rightarrow \lambda_2=\lambda_1 \times 0.7=6000 \times 0.7=4200 Å \end{gathered} $$

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

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