In a Young's double-slit experiment, the angle that locates the second dark fringe on either side of the central bright fringe is 7.2°. Find the ratio d/λ of the slit separation d to the wavelength λ of the light.
(m+1/2)/sin(theta) = d/lambda where m=1
tan(α/2) =x/L => x=L tan(α/2)
Coordinate of the second dark fringe is
x=(2k+1)Lλ/d
L tan(α/2)= (2k+1)Lλ/d
d/λ =(2k+1)/tan(α/2)= (2•2+1)/tan3.6°=79.5
To find the ratio d/λ (the slit separation d to the wavelength λ of the light), we can use the formula:
L = λD / d
where L is the distance between the screen and the double-slit, D is the distance between the double-slit and the source, λ is the wavelength of light, and d is the slit separation.
In a Young's double-slit experiment, the angle that locates the second dark fringe on either side of the central bright fringe is given by:
θ = λ / d
Given that the angle θ is 7.2°, we can convert it to radians:
θ = (7.2° * π) / 180°
Now, we can rearrange the formula to solve for d/λ:
d/λ = λ / θ
Substituting the value of λ and θ into the equation:
d/λ = λ / ((7.2° * π) / 180°)
Simplifying:
d/λ = λ / (0.126π)
Therefore, the ratio d/λ is λ / (0.126π).
To find the ratio d/λ of the slit separation d to the wavelength λ of light, we can use the equation for the fringe separation in Young's double-slit experiment.
The equation is given by:
λ = (d * sinθ) / m
Where:
λ is the wavelength of light,
d is the slit separation,
θ is the angle from the central bright fringe to the desired fringe,
and m is the order of the fringe.
In this case, we are given that the angle θ is 7.2° (converted to radians, this is approximately 0.1257 radians). We know that for the second dark fringe, m = 2.
Substituting the known values into the equation, we have:
λ = (d * sin(0.1257)) / 2
To find the ratio d/λ, we need to rearrange the equation to solve for d/λ. Multiply both sides of the equation by 2 and divide both sides by sin(0.1257), we have:
d/λ = 2λ / sin(0.1257)
Now, we can calculate the value of d/λ by substituting the known value of λ (wavelength).