In young's double slit experiment, the 10th maximum of wavelength `lambda_(1)`, is at a distance of `y_(1)` from the central maximum. When the wavelength of the source is changed to `lamda_(2)`, `5^(th)` maximum is at a distance of `y_(2)` from its central maximum. The ratio `( y_(1)/y_(2) )` is

Options

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

Answer

a

Explanation

The condition to form a bright band at a point is given by,`y=(n lambda D)/d`
For `y_(1):Y_(1)=(nlambda_(1)D)/d (because n=10)`
`implies y_(1)=(10lambda_(1)D)/d`
For `y_(2):Y_(2)=(nlambda_(2)D)/d (because n=5)`
`implies y_(2)=(5lambda_(2)D)/d`
`implies y_(1)/y_(2)=((10lambda_(1)d))/((5lambda_(2)D)/d)`
`therefore y_(1)/y_(2)=(2lambda_(1))/lambda_(2)`