Answer:
[tex]396[/tex] nm
Explanation:
As we know that
[tex]dsin\theta = m\lambda[/tex]
Given
Fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light
Therefore , [tex]m\lambda[/tex] value for fifth order maximum of red light will be equal to the third order maximum of red light
For fifth order maximum of red light
[tex]m\lambda = 5 * \lambda[/tex]
For fifth order maximum of red light
[tex]m\lambda = 3 * 660[/tex]
[tex]3 * 660 = 5 *\lambda\\\lambda = \frac{3*660}{5} \\\lambda = 396[/tex]nm
The value of unknown wavelength is of 396 nm.
Given data:
The wavelength of red light is, [tex]\lambda = 660 \;\rm nm =660 \times 10^{-9} \;\rm m[/tex].
The fifth order overlaps the third order maximum.
The concept involved in the solution of this problem is that since fifth-order maximum exactly overlaps the third-order maximum of the red light . Therefore, the value of [tex]a sin \theta[/tex] for the fifth order maxima is equal to that of third order maxima.
For third order maxima,
[tex]a sin\theta = m \lambda \\a sin\theta = 3 \times 660[/tex]
Here, a is the slit-width and [tex]\theta[/tex] is the angular separation.
And for the fifth order maxima,
[tex]a sin \theta = m \lambda\\a sin \theta = 5 \lambda[/tex]
Solving as,
[tex]5 \lambda = 3 \times 660\\\\\lambda = 396 \;\rm nm[/tex]
Thus, the value of unknown wavelength is of 396 nm.
Learn more about the diffraction here:
https://brainly.com/question/12290582
