In Young's double slit, 18 fringes are observed to be formed in a certain segment of the screen when light of wavelength 400 nm is used. If the wavelength is changed to 600 nm, the number of fringes observed in the same segment of the screen is

Step-by-step solution

Let the length of the segment on the screen be y . The fringe width is given by = D d . The number of fringes n in the segment y is n = y = y d D . This implies that n = constant , or n₁ ₁ = n₂ ₂ . Given n₁ = 18 , ₁ = 400 nm , and ₂ = 600 nm . Substituting the values, we get: 18 400 = n₂ 600 n₂ = 18 400 600 = 12 Thus, 12 fringes will be observed in the same segment. Answer: 12