Respuesta :
Answer:
[tex]\lambda_{B}=414.67 nm[/tex]
Explanation:
In this question we have given
[tex]\lambda_{A}=622nm[/tex]
we have to find
[tex]\lambda_{B}=?[/tex]
We know that
optical path difference for bright fringe is given as[tex]=n\lambda [/tex]
Here,
n is order of fringe
and optical path difference for dark fringe is given as[tex]=(n+.5)\lambda [/tex]
since the light with wavelength [tex]\lambda_{A}[/tex] produces its third-order bright fringe at the same place where the light with wavelength [tex]\lambda_{B}[/tex] produces its fourth dark fringe
it means
optical path difference for 3rd order bright fringe= optical path difference for forth order dark fringe
Therefore,
[tex]3\lambda_{A}=(4+.5)\lambda_{B}[/tex]...............(1)
Put value of [tex]\lambda_{A}[/tex] in equation (1)
[tex]3 \times 622=(4+.5)\lambda_{B}[/tex]
[tex]1866=4.5\lambda_{B}[/tex]
[tex]\lambda_{B}=414.67 nm[/tex]
The unknown wavelength of this laser light is equal to 415 nanometer.
Given the following data:
Wavelength A = 622 nm.
Wavelength B = ?
How to calculate the unknown wavelength.
In order to determine the unknown wavelength of the laser light, we would apply the interference experiment.
Mathematically, the interference experiment for bright fringe is given by this formula:
[tex]y_m =\lambda m[/tex]
Where:
- m is the order of fringe.
- [tex]\lambda[/tex] is the wavelength.
Similarly, the interference experiment for dark fringe is given by:
[tex]y_m =\lambda (m+0.5)[/tex]
With respect to the central or zeroth-order bright fringe, we have:
[tex]m\lambda_A =\lambda_B (m+0.5)\\\\3\times 622=\lambda_B (4+0.5)\\\\1866=4.5 \lambda_B\\\\\lambda_B=\frac{1866}{4.5}[/tex]
Wavelength B = 414.67 ≈ 415 nm.
Read more on wavelength here: brainly.com/question/14702686
