Q32 / 107 · NTA Abhyas (JEE Main) 2020 · Physics · Wave Optics

An interference is observed due to two coherent sources A and B separated by a distance 4λ along Y-axis where λ is the wavelength of the light source used. A detector D is moved along the positive X-axis. Find the total number of maxima points are observed on the X-axis excluding the points x=0 and x=∞?

Figure

Correct answer: 3

Solution

To obtain maxima the path difference

AD-BD=nλ

AD-xn=nλ

AD=nλ+xn ...(i)

Form ∆le ABD,

AD2=AB2+BD2

nλ+xn2=16λ2+xn2

n2λ2+xn2+2nλxn=16λ2+xn2

2nλxn=16-n2λ2

xn=16-n2λ2n

For n=0⇒x0=∞

n=1⇒x1=16-12λ=15λ2=7.5λ

n=2⇒x2=16-12λ=12λ4=3λ

n=3⇒x3=16-96λ=7λ6

n=4⇒x4=16-162×4λ=0

So the total no. of maxima points observed are 3.

Hence, the correct answer is 3.

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