In Young's double slit experiment, the 8th maximum with wavelength `lambda_1` is at a distance `d_1` from the central maximum and the 6th maximum with a wavelength `lambda_2` is at a distance `d_2`. Then `(d_1//d_2)` is equal to

Options

A. `(4)/(3)((lambda_(2))/(lambda_(1)))`
B. `(4)/(3)((lambda_(1))/(lambda_(2)))`
C. `(3)/(4)((lambda_(2))/(lambda_(1)))`
D. `(3)/(4)((lambda_(1))/(lambda_(2)))`

Answer

B

Explanation

Position of nth maxima from central maxima is given by `x_(n) = (n lambda D)/(d)`
For 8th maxima `x_(8) = (8lambda_(1)D)/(d_(1))`
and for 6th maxima `x_(6) = (6lambda_(2)D)/(d_(2))`
Now, `x_(6) = x_(8) , implies (d_(1))/(d_(2)) = (n_(1)lambda_(1))/(n_(2)lambda_(2))= (4)/(3) ((lambda_(1))/(lambda_(2)))`