Question

In a double-slit experiment, the third-order maximum for light of wavelength 490 nm is located 15 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 670 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of this light be located?

Answer 1

Answer:

The distance from the central bright spot are $156.8\times10^{-3}\ mm$ and $142.9\times10^{-3}\ mm$.

Explanation:

Given that,

Wavelength = 490 nm

Distance y= 15 mm

Length L=1.6 m

New wavelength = 670

We need to calculate the distance from the central bright spot

Using formula of distance

$y= \dfrac{m\lambda L}{d}$

$d=\dfrac{m\lambda L}{y}$

Put the value into the formula

$d=\dfrac{3\times490\times10^{-9}\times1.6}{15\times10^{-3}}$

$d=156.8\times10^{-6}\ m$

$d=156.8\times10^{-3}\ mm$

We need to calculate the distance from the central bright spot for new wavelength

Using formula of distance

$d=\dfrac{m\lambda L}{y}$

Put the value into the formula

$d=\dfrac{2\times670\times10^{-9}\times1.6}{15\times10^{-3}}$

$d=142.9\times10^{-6} m$

$d=142.9\times10^{-3}\ mm$

Hence, The distance from the central bright spot are $156.8\times10^{-3}\ mm$ and $142.9\times10^{-3}\ mm$.