A parallel beam of green light of wavelength 546 rim passes through a slit of width 0.40 mm. The transmitted light is collected on a screen 40 cm away. Find the distance between the two first order minima.
Answers
Answer:
The answer will be 5460 mm
Explanation:
It is given that the wavelength of the light, λ= 546 rim
The slit width , d = 0.40 mm
And it is collected on a screen at a distance of D= 40 cm = 4 mm
Let the angle between two first order minima is θ
Now for diffraction we know that the condition for making minima is
Δx = nλ [ where Δx is the path difference]
Now we know that slit difference, d
therefore sinθ = Δx /d
=> Δx = d sinθ
Now for first minima n= 1
therefore , Δx = λ
Hence,d sinθ =λ
=>sinθ = λ/d
Now as θ is very small we can take sinθ as tanθ
Therefore the if x is the distance between two minima then at θ it is x/2
Therefore we can say tanθ = x/D = λ/d
=> x = λ x D /d
= 546 x 4 / 0.40 = 5460 mm