Question

Your friend has been given a laser for her birthday. Unfortunately, she did not receive a manual with it and so she doesn't know the wavelength that it emits. You help her by performing a double-slit experiment, with slits separated by 0.18 mmmm. You find that two adjacent bright fringes are 4.9 mmmm apart on a screen 1.4 mm from the slits.

Answer 1

6.3*10^-7m

Step-by-step explanation:

to find the wavelength of the laser you can use the following formula:

`y=(m\lambda D)/(d)`

y: height from the center of the screen to a fringe

m: order of the fringe

D: distance to the screen = 1.4m

d: distance between slits = 0.18mm

you know the separation of two fringes. Hence, you can use two consecutive fringes to find the wavelength in the following way:

`\Delta y=(m\lambda D)/(d)-((m-1)\lambda D)/(d)=(\lambda D )/(d)\\\\\lambda=(\Delta y d)/(D)=((4.9*10^(-3)m)(0.18m*10^(-3)m))/(1.4m)=6.3*10^(-7)m`

hence, the walength is 6.3*10^-7m

Answer 2

`\lambda=630 nm`

Step-by-step explanation:

The equation of the fringe in a double slit experiment is given by:

`y=(m\lambda D)/(d)` (1)

here:

• y is the distance between bright fringes (two adjacent bright fringes distance = 4.9 mm).
• m is a natural number, related to the bright fringes in a diffraction pattern, in our case we use m=1
• D is the distance between the screen and the double slit (D=1.4 m)
• d is the distance between the slits (d=0.18 mm)
• λ is the wave length of the laser.

Therefor we just need to solve the equation (1) for λ:

`\lambda=(d*y)/(D)`

`\lambda=(0.00018*0.0049)/(1.4)`

`\lambda=6.3*10^(-7)m`

`\lambda=630 nm`

I hope it helps you!