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White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance `d (gt gtb)` from the slits At a point on the screen directly in front of one of the slits, certain wavelengths are missing some of these missing wavelengths are

A

`lamda=b^(2)//d`

B

`lamda=2b^(2)//d`

C

`lamda=b^(2)//3d`

D

`lamda=2b^(2)//3d`

Text Solution

Verified by Experts

The correct Answer is:
AC

Separation between slits=b, screen distance d
`(gt gt b)`
Path difference at `O` must be odd multiple of `(lamda)/(2)`
for missing wavelength `S_(2)O-S_(1)O=(nlamda)/(2)`
`impliessqrt(d^(2)+b^(2))-d=(nlamda)/(2)`
`impliesd^(2)+b^(2)=d^(2)+(n^(2)lamda^(2))/(4)+2xx(nlamda)/(2)xxd`
`implieslamda=(b^(2))/(nd)(n=1,3,5)`
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Knowledge Check

  • White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance d (gtb) from the slits. At a point on the screen directly in front of one of the slits, certain wavelength are missing. Some of these missing wavelength are

    A
    `lamda=(b^(2))/(d)`
    B
    `lamda=(2b^(2))/(d)`
    C
    `lamda=(b^(2))/(3d)`
    D
    `lamda=(2b^(2))/(3d)`

  • White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance d(gtgtb) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelength are (a) lambda = b^2//d (b) lambda=2b^2//d (c) lambda = b^2//3d (d)lambda = 2b^2//3d .

    A
    `lambda = b^2//d`
    B
    `lambda = 2b^2//d`
    C
    ` lambda = b^2//3d`
    D
    `lambda = 2b^2//3d`

  • White light is used to illuminate the two slits in Young's double slit experiment. The separation between the slits is b and the screen is at a distance Dgt gt b from slits. At a point on the screen directly in front of one of the slits, the missing wavelengths are

    A
    `(b^(2))/D,(b^(2))/(3D)`
    B
    `b/(D^(2)),b/(3D^(2))`
    C
    `(b^(2))/(2D),(b^(2))/(4D)`
    D
    `(D^(2))/b,(D^(2))/(3b)`

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