When light of wavelength 495 nm passes through a single slit of unknown width, the diffraction pattern displays a fourth-order maximum where the third minimum of light of an unknown wavelength had been observed to fall. What is the unknown wavelength
To find the unknown wavelength, we can use the concept of diffraction and the relationship between the position of the diffraction pattern maxima and the slit width.
First, let's understand the basics of diffraction. When light passes through a single slit, it spreads out and creates a pattern of bright and dark regions on a screen. The bright regions are known as maxima, and the dark regions are known as minima.
The position of the maxima is given by the formula:
dsinθ = mλ
Where:
- d is the width of the slit
- θ is the angle between the line drawn from the center of the slit to the maximum and the direction of the incident light
- m is the order of the maximum
- λ is the wavelength of light
Now, in our given scenario, we know that the fourth-order maximum for light of wavelength 495 nm coincides with the position of the third minimum for light of the unknown wavelength. This means that the angles and orders are the same for both cases.
So, we can write the following equation for the fourth-order maximum with the known wavelength (495 nm):
d * sin(θ) = 4 * (495 nm)
Now, for the unknown wavelength, the third minimum occurs at the same angle, so we can rewrite the equation with the unknown wavelength (let's call it λx):
d * sin(θ) = 3 * λx
Since both equations describe the same angle and the same slit width, we can set them equal to each other:
4 * (495 nm) = 3 * λx
Simplifying the equation, we find:
λx = (4 * 495 nm) / 3
Now, we can calculate the unknown wavelength:
λx = (4 * 495 nm) / 3 = 660 nm
Therefore, the unknown wavelength is 660 nm.