Question

1) Green light has a wavelength of approximately 510 nm. When green light is diffracted through a single slit with a width of 30 mm, the observed separation of the first dark fringe and the central maximum is 3.6 cm. Determine the distance between the slit and the screen for this observation to have been made2)Calculate the wavelength of the light that produces dark fringes 5.95 x 10-3 m apart on a screen 2.25 m away after passing through two slits that are spaced 0.100 mm apart3) Two sources are 7.2 cm apart and vibrate in phase at 7.0 Hz. A point on the third nodal line is 25.0 cm from one source and 27 cm from the other.(a) Calculate the wavelength of the waves.(b) Calculate the speed of the waves

Answer 1

`2117.65\text{ }m`

Step-by-step explanation

1) Parameters given

The wavelength of green light, λ = 510 nm

Width of the slit, a = 30 mm

Distance between the first fringe and central maximum, y = 3.6 cm

To find the distance between the slit and the screen, we have to apply the formula for the distance between the fringes and the maximum:

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

where m = 1

D = distance between the slit and the screen

Therefore, solving for D, the distance between the slit and the screen is:

`\begin{gathered} 0.036=(1*510*10^(-9)*D)/(30*10^(-3)) \\ \\ 0.036*30*10^(-3)=510*10^(-9)*D \\ \\ D=(0.036*30*10^(-3))/(510*10^(-9)) \\ \\ D=(1.08*10^(-3))/(5.1*10^(-7)) \\ \\ D=2117.65\text{ }m \end{gathered}`

That is the answer.