Question

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

Answer 1

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: 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:

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

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:

                                                $y\approx\frac{m\lambda D}{d} =\frac{m2\lambda D}{2d}$