$A$ linear aperture whose width is $0.02\, cm$ is placed immediately in front of a lens of focal length $60\, cm.$ The aperture is illuminated normally by a parallel beam of wavelength $5 \times 10^{-5}\, cm.$ The distance of the first dark band of the diffraction pattern from the centre of the screen is .....$cm$

  • A
    $0.20$
  • B
    $0.15$
  • C
    $0.10$
  • D
    $0.25$

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$A$ single slit diffraction experiment is performed to determine the slit width using the equation,$\frac{b d}{D} = m \lambda$,where $b$ is the slit width,$D$ is the distance between the slit and the screen,$d$ is the distance between the $m^{\text{th}}$ diffraction maximum and the central maximum,and $\lambda$ is the wavelength. $D$ and $d$ are measured with scales of least count of $1 \ cm$ and $1 \ mm$,respectively. The values of $\lambda$ and $m$ are known precisely to be $600 \ nm$ and $3$,respectively. The absolute error (in $\mu m$) in the value of $b$ estimated using the diffraction maximum that occurs for $m=3$ with $d=5 \ mm$ and $D=1 \ m$ is $.....$

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