Light from a 550 nm source goes through two slits 0.040 mm apart, a screen is 1.5 m from the slits.
a)what is the angular separation of the of the two first order maxima occurring on the screen?
b)what is the distance between the two first order maxima occuring on the screen?
c)what is the difference of the paths from the slits to a point on the screen where the fourth order maxima occurs.
What is it about this question that you need help with? This is a standard formula.
i don't understand the concept. i make sense of things by simplifying it to a meaning i can comprehend. with this question i can not do that.
To find the answers to these questions, we can use the concept of interference and the equation for the angular separation of maxima.
a) The angular separation of the two first-order maxima can be calculated using the formula for the angular separation of two adjacent maxima:
θ = λ / d
where θ is the angular separation, λ is the wavelength of light, and d is the distance between the two slits.
In this case, the wavelength of light is given as 550 nm (or 550 x 10^-9 m) and the distance between the slits is 0.040 mm (or 0.040 x 10^-3 m). Plugging these values into the formula:
θ = (550 x 10^-9 m) / (0.040 x 10^-3 m)
Simplifying the calculation:
θ = 13.75 x 10^-6 rad
b) The distance between the two first-order maxima can be calculated using the formula for the distance between adjacent maxima:
y = mλL / d
where y is the distance between the maxima, m is the order of the maxima (1 in this case), λ is the wavelength of light, L is the distance from the slits to the screen.
In this case, the wavelength of light is given as 550 nm (or 550 x 10^-9 m) and the distance from the slits to the screen is 1.5 m. Plugging these values into the formula:
y = (1 x 550 x 10^-9 m x 1.5 m) / (0.040 x 10^-3 m)
Simplifying the calculation:
y ≈ 20.63 x 10^-3 m (or 20.63 mm)
c) The difference in the paths from the slits to a point on the screen where the fourth-order maxima occurs can be calculated using the formula:
ΔL = (mλ) / 2
where ΔL is the difference in path lengths, m is the order of the maxima (4 in this case), and λ is the wavelength of light.
Using the given wavelength of 550 nm (or 550 x 10^-9 m), and plugging in the value of m:
ΔL = (4 x 550 x 10^-9 m) / 2
Simplifying the calculation:
ΔL = 1.1 x 10^-6 m (or 1.1 μm)