Blue light of wavelength λ passes through a single slit of width d and forms a diffraction pattern on a screen. If we replace the blue light by red light of wavelength 2λ , we can retain the original diffraction pattern if we change the slit widtha) to d/4b) to d/2c) not at alld) to 2de) to 4d

The diffraction pattern of a single slit has a bright central maximum and dimmer maxima on either side. We will retain the original diffraction pattern on a screen if the relative spacing of the minimum or maximum of intensity remains the same when changing the wavelength and the slit width simultaneously.

Using the following parameters: y for the distance from the center of the bright maximum to a place of minimum intensity, m for the order of the minimum, λ for the wavelength, D for the distance from the slit to the screen where we see the pattern and d for the slit width. The distance from the center to a minimum of intensity can be calculated with:

[tex]y\approx\frac{m\lambda D}{d}[/tex]

From the above expression we see that if we replace the blue light of wavelength λ by red light of wavelength 2λ in order to retain the original diffraction pattern we need to change the slit width to 2d:

[tex]y\approx\frac{m\lambda D}{d} =\frac{m2\lambda D}{2d}[/tex]

jayilych4real jayilych4real · Answer 2 · 2022-03-29T16:03:23+02:00

If we replace the blue light by red light of wavelength 2λ, then we can retain the original diffraction pattern if we change the slit width to d) 2d.

What is Wavelength?

This refers to the distance between successive crests of a wave.

Hence, we can see that the diffraction pattern has a bright central maximum and this can be retained on a screen if the relative spacing remains the same.

The distance can be calculated using:

y= mλD/d

Hence, we see that if we replace the blue light of wavelength λ by red light of wavelength 2λ, there would be a change the slit width to 2d in order to retain the original diffraction pattern and this would be represented as y= m2λD/2d