Light with a wavelength of 500 nm (5. 10-7 m) is incident upon a double slit with a separation of 0.28 mm (2.80 10-4 m). A screen is located 2.7 m from the double slit. At what distance from the center of the screen will the first bright fringe beyond the center fringe appear?
answer in mm
To find the distance from the center of the screen where the first bright fringe beyond the center fringe appears, we can use the formula for the position of the bright fringes in a double-slit interference pattern:
y = (λL) / d
where:
- y is the distance from the center of the screen where the bright fringe appears
- λ is the wavelength of light (500 nm = 5.00 × 10^-7 m)
- L is the distance between the screen and the double slit (2.7 m)
- d is the separation between the slits (0.28 mm = 2.8 × 10^-4 m)
Plugging in the values into the equation, we get:
y = (5.00 × 10^-7 m × 2.7 m) / (2.8 × 10^-4 m)
y = 1.35 × 10^-6 m / 2.8 × 10^-4 m
y ≈ 4.822 × 10^-3 m
To convert this to mm, we can multiply by 1000:
y ≈ 4.822 × 10^-3 m × 1000 = 4.822 mm
Therefore, the first bright fringe beyond the center fringe will appear approximately 4.822 mm from the center of the screen.
To find the distance from the center of the screen where the first bright fringe beyond the center fringe appears, we can use the equation for the location of bright fringes in a double-slit interference pattern:
dsinθ = mλ
Where:
- d is the separation between the double slits (0.28 mm)
- θ is the angle between the line connecting the center of the screen to the fringe and the line perpendicular to the screen (in this case, we can assume it to be small, so we can use the small-angle approximation: tanθ ≈ sinθ)
- m is the order of the fringe (in this case, we are looking for the first fringe beyond the center, so m = 1)
- λ is the wavelength of the light (500 nm or 5.0 x 10^(-7) m)
Rearranging the equation to solve for θ:
θ = sin^(-1)(mλ / d)
Substituting the values:
θ = sin^(-1)((1)(5.0 x 10^(-7) m) / (2.80 x 10^(-4) m))
Now we can calculate the value of θ.