Monochromatic light of wavelength 6560 Ao falls normally on a grating 2 cm wide. The first order spectrum is produced at an angle of 16o12' from the normal. Calculate the total no. lines on the grating
Best answer
Answer: Total number of lines on the grating \(\approx 8506\)
Grating equation for first order: \((a+b)\sin\theta = \lambda\).
\(\lambda = 6560\ \text{Å} = 6.56 \times 10^{-5}\) cm, \(\theta = 16^\circ 12' = 16.2^\circ\), \(\sin 16.2^\circ = 0.2790\).
\((a+b) = \dfrac{6.56 \times 10^{-5}}{0.2790} = 2.351 \times 10^{-4}\ \text{cm}\)
Lines per cm \(= \dfrac{1}{2.351 \times 10^{-4}} = 4253\)
Total lines on the 2 cm wide grating \(= \dfrac{2}{2.351 \times 10^{-4}} = 8506\)
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