The distance between two slits is 1.50 ×
M.A beam of coherent light of wavelength 600 nm illuminates these slits,and the distance between the slit and the screen is 2.00 m.What is the distance on the screen between the central bright fringe and the fourth-order bright fringe?
A)0.132 m
B)0.201 m
C)0.324 m
D)0.528 m
E)0.688 m

Question

The distance between two slits is 1.50 × 
M.A beam of coherent light of wavelength 600 nm illuminates these slits,and the distance between the slit and the screen is 2.00 m.What is the distance on the screen between the central bright fringe and the fourth-order bright fringe?
A)0.132 m 
B)0.201 m 
C)0.324 m 
D)0.528 m 
E)0.688 m

Quizplus · Accepted Answer

We can use the formula for the distance between bright fringes:
d sin θ = mλ
where d is the distance between the slits, θ is the angle from the central maximum to the fringe, m is the order of the fringe, and λ is the wavelength of light.

For the central maximum, we have:
d sin θ = 0λ
sin θ = 0
θ = 0

So the central maximum is in the center of the screen.

For the fourth-order maximum, we have:
d sin θ = 4λ
sin θ = 4λ/d

Using the small angle approximation (sin θ ≈ θ), we can find the distance between the central maximum and the fourth-order maximum on the screen:
θ ≈ 4λ/d
y ≈ Lθ = L(4λ/d)
y ≈ 2 (4λ/d)
y ≈ 0.324 m

So the distance on the screen between the central bright fringe and the fourth-order bright fringe is 0.324 m. The best choice is C.

The Distance Between Two Slits Is 1