Question

In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slits. If I_m be the maximum intensity, the resultant intensity I when they interfere at phase difference φ is given by

$straight I subscript straight m over 9 left parenthesis 4 space plus 5 space cos space straight ϕ right parenthesis$
$straight I subscript straight m over 3 open parentheses 1 space plus space 2 space cos squared space straight ϕ over 2 close parentheses$
$straight I subscript straight m over 5 open parentheses 1 space plus 4 space cos squared straight ϕ over 2 close parentheses$
$straight I subscript straight m over 9 open parentheses 1 plus 8 space cos squared space straight ϕ close parentheses$

Solution

straight I subscript straight m over 9 open parentheses 1 plus 8 space cos squared space straight ϕ close parentheses

Let A₁ = A₀, A₂ = 2A₀
If amplitude of resultant wave is A then
$straight A squared space equals space straight A subscript 1 superscript 2 space plus space straight A subscript 2 superscript 2 space plus 2 straight A subscript 1 straight A subscript 2 space cos space straight ϕ$
For maximum intensity
$straight A subscript max superscript 2 space equals space straight A subscript 1 superscript 2 space plus space straight A subscript 2 superscript 2 space plus 2 straight A subscript 1 straight A subscript 2 therefore fraction numerator straight A squared over denominator straight A subscript max superscript 2 end fraction space equals space fraction numerator straight A subscript 1 superscript 2 space plus straight A subscript 2 superscript 2 space plus 2 straight A subscript 1 straight A subscript 2 space cos space straight ϕ over denominator straight A subscript 1 superscript 2 space plus straight A subscript 2 superscript 2 space plus space 2 straight A subscript 1 straight A subscript 2 end fraction space equals space fraction numerator straight A subscript 0 superscript 2 space plus space 4 straight A subscript 0 superscript 2 space plus space 2 left parenthesis straight A subscript 0 right parenthesis left parenthesis 2 straight A subscript 0 right parenthesis cos space straight ϕ over denominator straight A subscript 0 superscript 2 space plus space 4 straight A subscript 0 superscript 2 space plus space 2 left parenthesis straight A subscript 0 right parenthesis left parenthesis 2 straight A subscript straight o right parenthesis end fraction straight I over straight I subscript straight m space equals space fraction numerator 5 space plus 4 space cos space straight ϕ over denominator 9 end fraction space equals space fraction numerator 1 space plus space 8 space cos squared space left parenthesis straight ϕ divided by 2 right parenthesis over denominator 9 end fraction$

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Wave Optics

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Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

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