Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.81 m away. If the first-order maxima are separated by 1.40 m on the screen, what is the distance between the two second-order maxima?
To find the distance between the two second-order maxima, we first need to determine the angular separation between adjacent maxima.
The angular separation between adjacent maxima can be determined using the formula:
sinθ = mλ / d
where θ is the angular separation, m is the order of the maxima, λ is the wavelength of the light, and d is the spacing between the grating lines.
Since the light strikes the diffraction grating at normal incidence, the angle θ is zero. Therefore, sinθ is also zero, which means that the denominator of the equation is zero:
0 = mλ / d
Therefore, for the first-order maxima, m = 1. For the second-order maxima, m = 2.
First, let's find the wavelength of the light. Since we are given that the light is monochromatic, we can use the formula:
λ = distance between adjacent maxima / order of maxima
λ = 1.40 m / 1 = 1.40 m
Now that we have the wavelength, we can find the distance between the two second-order maxima using the same formula:
distance between adjacent maxima = λ * order of maxima
distance between adjacent maxima = 1.40 m * 2 = 2.80 m
Therefore, the distance between the two second-order maxima is 2.80 m.