Respuesta :
Answer:
N = 221.4 lines / mm
Explanation:
Given:
- The wavelength of the source λ = 670 nm
- Distance of the grating from screen B = 40.0 cm
- The distance of first bright fringe from central order P = 6.0 cm
Find:
How many lines per millimeter does this grating have?
Solution:
- The derived results from Young's experiment that relates the order of bright fringes about the central order is given by:
sin (Q) = n*λ*N
Where,
n is the order number 0, 1 , 2, 3 , ....
λ is the wavelength of the light source
Q is the angle of sweep respective fringe from central order
N is the number of lines/mm the grating has
- We will first compute the length along which the light travels for the first bright fringe:
L^2 = P^2 + B^2
L^2 = 40^2 + 6^2
L^2 = 1636
L = 40.45 cm
- Now calculate the sin(Q) that the fringe makes with the central order:
sin (Q) = P / L
sin (Q) = 6 / 40.45
- Now we will use the derived results:
N = sin(Q) / n*λ
Where, n = 1 - First order
Plug values in N = (6 / 40.45) / (670 *10^-6)
N = 221.4 lines / mm
In the given case, the number of lines per millimeter this grating have - 223.9 lines per mm
Given:
The wavelength λ = 670 nm
Distance of the grating from screen L = 40.0 cm
The distance of first bright fringe from central order y = 6.0 cm
Solution:
- The derived results from Young's experiment that relates the order of bright fringes about the central order is given by:
with the method of small-angle approximation,
y = m(lam)(L)/d
and,
d = m(λ)(L)/y
Placing the given value
d = 1 x 670 x [tex]10^{-9}[/tex] x .4m / 0.06m
= 4.467 × [tex]10^{-6}[/tex]
Then lines per mm = 1/d
1/4.467× = lines per mm
= 223.9 lines per mm
Thus, In the given case, the number of lines per millimeter this grating have - 223.9 lines per mm
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