Question

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.

Answer 1

Answer:

The answer will be 5460 mm

Explanation:

According to the problem the wavelength of the light is 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 differenc, 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