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OverLord2011 [107]
3 years ago
14

Blue light of wavelength λ passes through a single slit of width d and forms a diffraction pattern on a screen. If we replace th

e 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
Physics
1 answer:
ololo11 [35]3 years ago
7 0

Answer:

We can retain the original diffraction pattern if we change the slit width to d) 2d.

Explanation:

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

                                                    y\approx\frac{m\lambda D}{d}

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:

<em>                                                 </em>y\approx\frac{m\lambda D}{d} =\frac{m2\lambda D}{2d}

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