Light from a sources emitting two wavelengths `lambda_(1)` and `lambda_(2)` is allowed to fall on Young's double-slit apparatus after filtering one of the wavelengths. The position of interference maxima is noted. When the filter is removed both the wavelengths are incident and it is found that maximum intensity is produced where the fourth maxima occured previously. If the other wavelength if filtered, at the same location the third maxima is found. What is the raito of wavelength?

Options

A. `(2)/(3)`
B. `(3)/(2)`
C. `(3)/(4)`
D. `(4)/(3)`

Answer

c

Explanation

The maxima in this case is obtained whenever
`x_(cm) = (n lambda D)/(d)`
` (x_(4)) lambda_(1) = (4 lambda_(1) D)/(d)`
This must be equal to `(x_(3)) lambda_(2) = (3 lambda_(2) D)/(d)`, since `(x_(4)) lambda_(1) = (x_(3)) lambda_(2)`.
`:. (4 lambda_(1) D)/(d) = 3 lambda_(2) (D)/(d) implies (lambda_(1))/(lambda_(2)) = (3)/(4)`
Hence, when both wavelengths are incident simultaneously, the maxima due to will coincide at a point where the fourth maxima due to `lambda_(1)` occured. This point will have maximum intensity and intensity will not be zero at any point.