Question

Two diffraction gratings, A and B, are located at the same distance from the observation screens. Light with the same wavelength λ is used for each. The separation between adjacent principal maxima for grating A is 2.7 cm, and for grating B it is 3.2 cm. Grating A has 2448 lines per meter. How many lines per meter does grating B have? (Hint: The diffraction angles are small enough that the approximation sin(θ) ~ tan(θ) can be used.)

Answer 1

The expression for the number of slits for B =
(Number of slits for A * separation between adjacent principal maxima for grating B) / (The separation between adjacent principal maxima for grating A )

Now given that -

no. of slits for A = 2448 lines/meter

separation for adjacent principal maxima for grating B = 3.2 cm

separation for adjacent principal maxima for grating A = 2.7 cm

put these values in the above expression -

number of slits for B = (2448 x 3.2) / 2.7 = 2901 lines per meter.