Question
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?
Answers
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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.
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.