In two separate set-ups of the young's double slit experiment fringes of equal width are observed when light of wavelengths in the ratio 1: 2 are used. If the ratio of the slit separation in the two cases is 2: 1 the ratio of the distances between the plane of the slits and the screen in the two set-ups is:

Question

In two separate set-ups of the young's double slit experiment fringes of equal width are observed when light of wavelengths in the ratio 1: 2 are used. If the ratio of the slit separation in the two cases is 2: 1 the ratio of the distances between the plane of the slits and the screen in the two set-ups is: (A) 4: 1 (B) 1: 1 (C) 1: 4 (D) 2: 1

Tardigrade Admin · Accepted Answer

β=(λ D / d )=(β1/β2)=(( D 1/ D 2))((λ1/λ2))(( d 2/ d 1)) ⇒ ( D 1/ D 2)=(4/1)

$4 : 1$

$1 : 1$

$1 : 4$

$2 : 1$

$β = \frac{λ D}{d} = \frac{β _{1}}{β _{2}} = (\frac{D _{1}}{D _{2}}) (\frac{λ _{1}}{λ _{2}}) (\frac{d _{2}}{d _{1}})$
$\Rightarrow \frac{D _{1}}{D _{2}} = \frac{4}{1}$

4:1

1:1

1:4

2:1

β=dλD​=β2​β1​​=(D2​D1​​)(λ2​λ1​​)(d1​d2​​) ⇒D2​D1​​=14​

$4 : 1$

$1 : 1$

$1 : 4$

$2 : 1$

$β = \frac{λ D}{d} = \frac{β _{1}}{β _{2}} = (\frac{D _{1}}{D _{2}}) (\frac{λ _{1}}{λ _{2}}) (\frac{d _{2}}{d _{1}})$
$\Rightarrow \frac{D _{1}}{D _{2}} = \frac{4}{1}$