You are conducting a single slit diffraction experiment with a light of wavelength λ. What appears , on a distant viewing screen, at a point at which the top and bottom rays through the slit have a path length difference equal to (a) 5λand (b) 4.5λ?

Short Answer

Expert verified
  1. A dark spot is observed.
  2. A bright spot is observed.

Step by step solution

01

The given data

A single slit diffraction experiment with a light of wavelengthλis conducted.

02

Concept and Formula used

The dark fringes can be located with the general equation

asinθ=mλfor m=1,2,3,...

‘a’ is path length difference of slit andλ is wavelength.

03

Take path length difference to be  5λ

(a)

Using the above equation, path length difference is5λ .

So role="math" localid="1663145683374" asinθ=5λ

Here, role="math" localid="1663145734474" m=5, a minima

Thus, a dark spot will be observed.

04

Take path length difference to be  4.5λ

b)

Using the above equation, path length difference is4.5λ .

So asinθ=4.5λ

Here, m=4.5

It is between 4th and 5th minima, so, this is at approximate maxima.

Thus, a bright spot will be observed.

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