Respuesta :
Answer:
Slit width is 0.109 mm
Solution:
As per the question:
Wavelength of the light, [tex]\lambda = 680\ nm = 680\times 10^{- 9}\ m[/tex]
Distance from the screen, D = 5.6 m
Bright band in the center, 2x = 8.1 cm
x = 4.05 cm
Now,
To calculate the slit width, w:
From the diffraction:
[tex]sin\theta = \frac{\lambda}{w}[/tex]
For small angle:
[tex]sin\theta[/tex] ≈ [tex]tan\theta = \frac{x}{D}[/tex]
Also
[tex]\frac{x}{D} = \frac{\lambda }{w}[/tex]
Thus
[tex]w = \frac{D}{x}\times \lambda[/tex]
Substituting appropriate values in the above eqn:
[tex]w = \frac{6.5}{4.05\times 10^{-2}}\times 680\times 10^{- 9}[/tex]
w = 0.109 mm
1. The width of the slit is 0.109 mm.
Calculation of the slit width:
Since λ=680nm i.e. [tex]= 680 \times 10^{-9}m[/tex]
distance ,D = 5.6m
Bright band in the center, 2x = 8.1 cm
So,
x = 4.05 cm
Here we used diffraction:
[tex]sin \theta = \lambda \div \omega\\\\sin \theta = tan \theta = x \div D\\\\x \div D = \lambda \div \omega\\\\\omega = D \div x \times \lambda\\\\= 6.5 \div 4.05 \times 10^{-2} \times 680 \times 10^{-9}[/tex]
= 0.109 mm
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