Red light with a wavelength of 660 nm and blue light with a wavelength of 480 nm are beamed at a double slit with a separation of 2x10^-3 mm. The third order maximums for the different colours occur at different spots. What is the angle between the second order maximums?
To find the angle between the second order maximums, we first need to determine the distances (y) of the maxima from the central maximum for each wavelength. We can use the formula for the position of the maxima in a double slit experiment:
y = m * λ * L / d
Where:
y = distance from central maximum
m = order of the maximum (m = 0 for the central maximum)
λ = wavelength of light
L = distance from the double slit to the screen
d = separation between the slits
Let's calculate the distances for each wavelength:
For red light with a wavelength of 660 nm (660 x 10^-9 m):
y_red = (0 * 660 x 10^-9) * L / (2 x 10^-3)
For blue light with a wavelength of 480 nm (480 x 10^-9 m):
y_blue = (0 * 480 x 10^-9) * L / (2 x 10^-3)
Since the orders for the maxima are different for red and blue light, we need to find the distances for the second order maximums. For the second order maximums, m = 2:
y_red_2nd = (2 * 660 x 10^-9) * L / (2 x 10^-3)
y_blue_2nd = (2 * 480 x 10^-9) * L / (2 x 10^-3)
Now we have the distances y_red_2nd and y_blue_2nd. To find the angle between these two maxima, we can use the small-angle approximation:
θ = y / L
Where θ is the angle and L is the distance from the double slit to the screen. Since y is the distance from the central maximum to the maximum, the angle represents the angle of deviation from the central maximum.
Let's calculate the angle between the second order maximums for red and blue light:
θ_red_blue_2nd = (y_red_2nd - y_blue_2nd) / L
By substituting the values of y_red_2nd, y_blue_2nd, and L into the equation, we can find the angle between the second order maximums for red and blue light.