Question

Deduce the missing order for double the rounhofer diffraction pattern, if the

slit width 0.16mm and they are 0.8mm spart​

Answer 1

Answer:

1900 nm.

Concept:

Fraunhofer diffraction pattern

Diffraction: Diffraction is the bending of light around the corners of the obstacles.

Given:

Slit width, d = 0.16 mm = 0.16 x 10⁻³ m

Distance between screeen and slits, D = 0.8 mm = 0.8 x 10⁻³ m

For wavelength, let us consider visible light. Wavelength, λ = 380 nm = 380 x 10⁻⁹ m

Find:

Missing order or Fringe width, β.

Solution:

Fringe width, β = $\frac{\lambda D}{d}$

$\beta = \frac{380\times10^{-9}(0.8\times10^{-3})}{0.16\times10^{-3}}$

$\beta = \frac{304\times10^{-9-3}}{0.16\times10^{-3}}$

$\beta = 1900\times10^{-9}$ m

$\beta = 1900 nm$

Hence, the missing order is 1900 nm.

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Answer 2

Concept introduction:

In optics, the Fraunhofer diffraction formula is used to simulate the diffraction of signals when the scattering is observed at the focus plane of an imaging lens as well as when it is viewed at a distant place from the scattering object (in the far-field area).

Given:

Here it is given that, Slit width $d = 0.16 mm = 0.16 * 10^{-3} m$.

Distance between screen and slits,  $D = 0.8 mm = 0.8 * 10^{-3} m$.

For wavelength, let us consider visible light. Wavelength,  

   λ$= 380 nm = 380 * 10^{-9} m$.

To find:

We have to find the Missing order or Fringe width, β.

Solution:

According to the problem,

Fringe width, β

$\beta =\frac{380*10^{-9}(0.8*10^{-3} ) }{0.16*10^{-3} } \\=1900*10^{-9}m\\ =1900nm$

Hence the missing order is $1900nm$.

Final answer:

So, the final answer of the question is -> $1900nm$.

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