In a single slit diffraction experiment, first minimum of red light (660 nm) coincides with the first maximum of some other wavelength λ . The value of λ in nm is:

Question

In a single slit diffraction experiment, first minimum of red light (660 nm) coincides with the first maximum of some other wavelength λ . The value of λ in nm is: (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The angular position of first minimum for red light of wavelength

λ_{r}

is given by

s in θ_{1} = \frac{λ _{r}}{a}

The angular position of first maximum for light of wavelength

λ^{^{'}}

is given by

s in θ_{1}^{^{'}} = \frac{3 λ ^{^{'}}}{2 a}

According to given condition,

s in θ_{1} = s in θ_{1}^{^{'}}

\Rightarrow \frac{λ _{r}}{a} = \frac{3 λ ^{^{'}}}{2 a}

\Rightarrow λ^{^{'}} = \frac{2 λ _{r}}{3}

= \frac{2}{3} \times 660

= 440 nm

Q. In a single slit diffraction experiment, first minimum of red light (660nm) coincides with the first maximum of some other wavelength λ . The value of λ in nm is:

Q. In a single slit diffraction experiment, first minimum of red light $(660 nm)$ coincides with the first maximum of some other wavelength $λ$ . The value of $λ$ in $nm$ is: