Monochromatic light of wavelength 605 nm falls on a slit of width 0.095 mm. The slit is located 40 cm from a screen. How far is the center of the central bright band to the first dark band?

Answer 1

We can find the distance from the center of the central bright band to the first dark band using the formula:

x = (λL) / a

where x is the distance we want to find, λ is the wavelength of the light, L is the distance from the slit to the screen, and a is the width of the slit.

First, we need to convert the given values to meters:

λ = 605 nm = 605 × 10^(-9) m
a = 0.095 mm = 0.095 × 10^(-3) m
L = 40 cm = 40 × 10^(-2) m

Now, we can plug the values into the formula:

x = (605 × 10^(-9) m) * (40 × 10^(-2) m) / (0.095 × 10^(-3) m)

x = (24200 × 10^(-11) m^2) / (0.095 × 10^(-3) m)

x ≈ 254736.842 × 10^(-8) m

x ≈ 0.02547 m = 2.547 cm

So, the distance from the center of the central bright band to the first dark band is approximately 2.547 cm.