Question

A laser with wavelength d/8 is shining light on a double slit with slit separation 0.500 mm. This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits. What is the wavelength λ of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.500 mm?

Answer 1

Answer:

0.000109375 m

Explanation:

d = Distance between grating = 0.5 mm

m = Order

$\lambda_1=\dfrac{d}{8}$

Minima relation

$m-\dfrac{1}{2}$

For fourth order minima

$dsin\theta=(4-\dfrac{1}{2})\lambda_1$

For second maxima

$dsin\theta=2\lambda_2$

From the two equations we get

$(4-\dfrac{1}{2})\lambda_1=2\lambda_2\\\Rightarrow \lambda_2=\dfrac{(4-\dfrac{1}{2})\lambda_1}{2}\\\Rightarrow \lambda_2=\dfrac{(4-\dfrac{1}{2})\dfrac{0.5\times 10^{-3}}{8}}{2}\\\Rightarrow \lambda_2=0.000109375\ m$

The wavelength is 0.000109375 m