n^th order Angular width of fringe in air,

sin(θ_n) = nλ/d … (1)

Where sin(θ) is angular fringe width

n is order of fringe

λ is wavelength of light used

d is slit width

When entire apparatus is taken into water, d and D remain same

∴ Angular fringe width for nth order in water,

sin(θ_n^w) = nλ^w/d … (2)

where λ^w is wavelength of the light in water

Taking ratio of equations (1) & (2)

sin(θ_n)/sin(θ_n^w) = λ/ λ^w

Refractive index of water is 4/3

i.e., 4/3 = c/v

Where c is velocity of light in air (vacuum) and v is velocity in water

c/v = ν λ /ν λ^w

Since frequency does not vary with medium, ν = ν^w

Thus 4/3 = λ/λ^w

Thus we have,

sin(θ)/sin(θ^w) = 4/3

sin(θ^w) = sin(θ) × 3/4

= 0.2 × 3/4 = 0.15°