Question

You find an unmarked blue laser on your way to physics class. When you get to class you realize that you can determine the wavelength of the laser by doing a double-slit experiment. Shining the laser through a double slit with a separation of 0.351 mm and projecting the interference pattern on the wall 2.17 m away, the first bright fringe is 2.85 mm from the center of the pattern. What is the wavelength?
nm

Answer 1

This problem is based on double slit experiment,

As we know, Fringe width

$\beta=\dfrac{D \lambda }{d}$ Here, D: Distance between the screen and slit

d: slit width

   $\lambda$ : Wavelength of light used

Also we know first maxima will be at a distance of $1\beta$ from the center.

therefore using the above condition, we get-

$2.85*10^{-3}=1\beta$

Using expression for $\beta$ we get,

$2.85*10^{-3}=1\dfrac{D \lambda}{d}$

$\lambda=2.85*10^{-3}\dfrac{d}{D*1}$

after using given values of D and d,

$\lambda=2.85*10^{-3}\dfrac{0.351*10^{-3}}{2.17*1}$

$\lambda=460.99*10^{-9}m$

$\lambda=461 nm$

Thankyou.