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Wave Optics: Diffraction through transmission grating.

I have this problem which I'm not sure how to do. I understand the diffraction grating and all the formulae that describe diffraction with only a grating but I'm not sure how to do calculation when a grating is in combination with a lens. Could you please just explain how I should do this problem, but don't do any calculations to save time. You can maybe just write the first line of what needs to be calculated and leave the rest to me. Don't spend time deriving the grating formulae or calculating the slit width as I could do that.

The problem is:

A diffraction grating has slits ruled on opaque material and has 20 slits per mm. The distance between the slit centres is twice the width of each slit. The grating is uniformly illuminated at normal incidence. The transmitted light passes through a lens of focal length 1 m and then onto a screen that lies 1 m from the lens. On the screen the first-order diffraction peak lies 10mm from the centre-line of the apparatus. Calculate the wavelength of the light and predict the location of the next visible diffraction peak.

Solution Preview

Please see the attached file.

A diffraction grating has slits ruled on opaque material and has 20 slits per mm. The distance between the slit centres is twice the width of each slit. The grating is uniformly illuminated at normal incidence. The transmitted light passes through a lens of focal length 1 m and then onto a screen that lies 1 m from the lens. On the screen the first-order diffraction peak lies 10mm from the centre-line of the apparatus. Calculate the wavelength of the light and predict the location of the next visible diffraction peak.

As light is considered a wave, every slit can be considered as a secondary source of light emitting waves in all directions. If ...

Solution Summary

The setup with a grating and the position of first order maximum is given. The wavelength of the incident beam and the position of the second order peak is estimated.

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