Single Slit Diffraction

At first minima, b sin

%5Ctheta%20%3D%5Clambda

%5Chspace%7B10mm%7D%20b%20%5C%2C%20%5Ctheta%3D%5Clambda%20%5C%2C%20or%20%5C%2C%20%5C%2C%20b%20%5Cbig(%5Cfrac%7B%5Clambda%7D%7BD%7D%5Cbig)%3D%5Clambda

%5Chspace%7B25mm%7D%20y%3D%5Cfrac%7B%5Clambda%20D%7D%7Bb%7D

%5Chspace%7B25mm%7D%20%5Cfrac%7Byb%7D%7BD%7D%3D%5Clambda%20%5Chspace%7B20mm%7D%20...%20(i)

Now, at P (First minima) path difference between the rays
reaching from two edges (A and B ) will be

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5CDelta%20x%3D%5Cfrac%7Byb%7D%7BD%7D%20%5Chspace%7B10mm%7D

(Compare with

%5CDelta%20x%3D%5Cfrac%7Byd%7D%7BD%7D

in YDSE)
or

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5CDelta%20x%3D%5Clambda%20%5Chspace%7B30mm%7D

[From E (i)]
Corresponding phase difference

(%5Cphi)

will be

%5Chspace%7B15mm%7D%20%5Cphi%3D%5Cbig(%5Cfrac%7B2%20%5Cpi%7D%7B%5Clambda%7D%20%5Cbig)%2C%5CDelta%20x%2C%5Cphi%3D%5Cfrac%7B2%20%5Cpi%7D%7B%5Clambda%7D.%5Clambda%3D2%20%5Cpi

I(%5Cphi)%3DI_1%2BI_2%2B2%20%5Csqrt%7BI_1%20I_2%7D%20cos%20%5C%2C%20%5Cphi%20%5Chspace%7B20mm%7D%20...(i)

Here,

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20I_1%3DI%20%5C%2C%20and%20%5C%2C%20I_2%3D4I

At point A,

%5Cphi%3D%5Cfrac%7B%5Cpi%7D%7B2%7D

%5Ctherefore%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20I_A%3DI%2B4I%3D5I

At point B,

%5Cphi%3D%5Cpi

%5Ctherefore%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20I_B%3DI%2B4I-4I%3DI

%5Ctherefore%20%5C%2C%20%5C%2C%20%5C%2C%20I_A-I_B%3D4I

NOTE E (i) for resultant intensity can be applied only when the
sources are coherent. In the question it is given that the rays
interfere. Interference takes place only when the sources are
coherent. That is why we applied equation number (i). When the
sources are incoherent, the resultant intensity is given by I =

I_1%2BI_2

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Single Slit Diffraction

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs