In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is:

Concept: 

In this we used young's double slit experiment:

λ = wavelength of beam, D = difference between slits and optical screen, d = distance between slits

distance between fringes = y = nλD/d   ---- (1)

the path difference = nλ    ---- (2)

Calculations: 

From equation 2 we know that when we use fringes of different wavelength in same path then path difference will remain same i.e.

⇒ n₁λ₁ = n₂λ₂      ---- (3)

Given: 

No. of fringes obtain by student (n₁) = 8

Wavelength of beam used by student (λ₁) = 600nm

Changed wavelength of beam (λ₂) = 400nm

No. of fringes obtained (n₂) = ?

from equation 3 we get:

n₁λ₁ = n₂λ₂ ⇒ 8 × 600 = n₂ × 400

n₂ = 12 ⇒ for wavelength of 400 nm we observed 12 number of fringes.

Hence option 1) is the correct choice.