In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to

CONCEPT:

Young's double experiment: In young's double-slit experiment the angular width of the fringe is written as;

\(β = \frac{λ D}{d}\)

Here, β is the angular width, D is the distance between screen and slits, 

λ is the wavelength and d is the separation distance of the slits.

CALCULATION:

As we know that Angular width, \(β = \frac{λ D}{d}\) ----(1)

Given: β 1 = 0.20°

 β ₂ = 0.21°

D = 100 cm

d₁ = 2 mm

Now, On using the equation (1) we get;

\(β_1 = \frac{λ D}{d_1}\) ----(2)

\(β_2 = \frac{λ D}{d_2}\) -----(3)

Now, On dividing equation (1) by equation (2) we have;

\(\dfrac {β_1}{β_2} = \frac{\frac{λ D}{d_1}}{\frac{λ D}{d_2}}\)

⇒ \(\dfrac {β_1}{β_2} = \frac{{d_2}}{{d_1}}\)

Now, On putting the given values we have,

, \(\frac{{0.20}}{{0.21}} = \frac{d_2}{{2mm}}\)

∴ d₂ = 1.9 mm

Hence, Option 2) is the correct answer.