A grating is used to form a diffraction pattern on a distant screen using green

Question

A grating is used to form a diffraction pattern on a distant screen using green light (gamma_green = 530 nm). If blue light (gamma_blue = 460 nm) is used instead, what will happen to the first order maxima on the screen?

Answer options: [a] Nothing will change about the first order maxima. [b] The first order maxima will disappear. [c] The spacing between the first order maxima will decrease. [d] The spacing between the first order maxima will increase. Please explain Thoroughly, I would appreciate it.

Explanation / Answer

ANS -> C)The spacing between the first order maxima will decrease

For a diffraction grating we have,

Displacement y = (Order m x Wavelength x Distance D)/(slit separation d)

Keeping everything else constant and just varying wavelength, the displacement or spacing will directly depend on wavelength i.e.

y is proportional to wavelength and hence for greater wavelength the spacing will be greater. Similarly for lower wavelength spacing will be less. This is why Diffraction Grating is used as a tool to separate colors from incident light, since different color light has different wavelength and gets diffracted to different places on screen.

In our case gamma_green(530nm) is replaced by gamma_blue(460nm) i.e. wavelength is reduced and hence the spacing between first order maxima will decrease.

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