Question

In a biprism experiment, the slit separation is 1 mm. Using monochromatic light of wavelength 5000 Å, an interference pattern is obtained on the screen. Where should the screen be moved? so that the change in fringe width is 12.5 x 10⁵ m? 

Options

• Away from the slit by 5 cm

• Away or towards the slit by 12.5 cm

• Towards the slit by 10 cm

• Away or towards the slit by 25 cm

Answer 1

Away or towards the slit by 25 cm

Explanation:

d = `1 xx 10^-3`m

`lambda = 5000 Å = 5 xx 10^-7`m

`beta_2 - beta_1 = 12.5 xx 10^-5`m

D₂ - D₁ = ?

`beta_1 = (lambdaD_1)/d`

`beta_2 = (lambdaD_2)/d`

`beta_2 - beta_1 = lambda/d(D_2 - D_1)`

∴ `(D_2 - D_1) = d/lambda(beta_2 - beta_1)`

`(D_2 - D_1) = (10^-3)/(5 xx 10^-7) xx 12.5 xx 10^-5 = 12.5/50 = 25  cm`