Question

1)

A laser beam is incident on two slits with separation d = 0.026 mm. A screen is placed L = 3.8 m from the slits. The wavelength of the laser light is λ = 4250 Å. θ₁ and θ₂ are the angles to the first and second bright fringes above the center of the screen.

a) Express sin(θ₁) in terms of d and λ: sin(θ₁) = ____________   

b) Express sin(θ₂) in terms of d and λ: sin(θ₂) = ____________

c) Express the distance between the two bright fringes on the screen, y, in terms of θ₁, θ₂ and L. y= ________________

d) Solve for the numerical value of y in meters.    y=___________

IX

2) A thin layer of oil with index of refraction n_o = 1.47 is floating above the water. The index of refraction of water is n_w = 1.3. The index of refraction of air is n_a = 1. A light with wavelength λ = 525 nm goes in from the air to oil and water.

a) Express the minimum thickness of the film that will result in destructive interference, t_min, in terms of λ_o. t_min = ______

b) Express t_min in terms of λ and n_o. t_min = ________

c) Solve for the numerical value of t_min in nm. t_min = ________

Answer 1

m *lu X L Sol. I> d= 0.026 mm , L= 3.8m = 4250 X10-10 -> If x, be the position of the first bright fringe on the screen, sino = > and for position X₂ of second bright fringe on the screen, sino = 쓴 a. Now, for the formection of first bright fringe, Path clifference =) : xd = = sino, d * L b. Similarly for second bright fringe, Xad = = sino 2L 2) d Ang ç Distance between two bright finges X2 -x, =Y => y=L(sino₂-sino, ) Aug d. y=L(sino-sino) 2 L 12/27 - 12) = 2 LA 2 3.8 x 4250 x10-10 0.026 X10-3 y = 0.062 m) Ang

Sol. 2 no=1.47 , X= 525 mm. -> The relation of wavelength & re fre. index is = no => do=^ 10 no => Thickness relation is, It= do 2 Ang to serve ::17: 1 Aug 2 no from the above ean thickness will be t = 525 X10-9 2 x 1.47 t = 178.57 nm _Ang