A Young's double slit has a slit separation of 2.50x10 raised to the -5th power m on which a monochromatic light beam is directed. The resultant bright fringes on a screen 1.00 m from the double slit are separated by 2.30x10 raised to the -2nd power m. What is the wavelength of this beam? (1nm = 10 raised to the -9th power m)
To find the wavelength of the beam, we can use the formula for calculating the fringe separation:
\[ \text{fringe separation (Δy)} = \frac{\lambda \cdot L}{d} \]
where:
- λ is the wavelength of the beam
- L is the distance from the double slit to the screen (1.00 m in this case)
- d is the slit separation (2.50 × 10^-5 m in this case)
Rearranging the formula to solve for λ, we get:
\[ \lambda = \frac{\text{fringe separation (Δy)} \cdot d}{L} \]
Now we can substitute the values into the formula:
\[ \lambda = \frac{2.30 × 10^{-2} \, \text{m} \cdot 2.50 × 10^{-5} \, \text{m}}{1.00 \, \text{m}} \]
Simplifying the expression:
\[ \lambda = 5.75 × 10^{-7} \, \text{m} \]
Therefore, the wavelength of the beam is 5.75 × 10^-7 m.
Final Note: To convert this to nanometers (nm), you can use the conversion factor provided: 1 nm = 10^-9 m. Therefore, the wavelength of the beam in nanometers is:
\[ \lambda = (5.75 × 10^{-7} \, \text{m}) \times \frac{1 \, \text{nm}}{10^{-9} \, \text{m}} \]
\[ \lambda = 575 \, \text{nm} \]