KCET · Physics · Wave Optics
Red light of wavelength \(625 \mathrm{~nm}\) is incident normally on an optical diffraction grating with \(2 \times 10^{5}\) lines \(/ \mathrm{m}\). Including central principal maxima, how many maxima may be observed on a screen which is far from the grating?
- A 15
- B 17
- C 8
- D 16
Answer & Solution
Correct Answer
(B) 17
Step-by-step Solution
Detailed explanation
For principal maxima in grating spectra
\[
\frac{\sin \theta}{\mathrm{N}}=\mathrm{n} \lambda
\]
where, \(\mathrm{n}=(1,2,3)\) is the order of principal maxima and \(\theta\) is the angle of diffraction.
\[
\mathrm{n}=\frac{1}{\lambda \mathrm{N}}=\frac{1}{6.25 \times 10^{-7} \times 2 \times 10^{5}}=8
\]
\(\therefore\) Number of maxima \(=2 \mathrm{n}+1=2 \times 8+1=17\)
\[
\frac{\sin \theta}{\mathrm{N}}=\mathrm{n} \lambda
\]
where, \(\mathrm{n}=(1,2,3)\) is the order of principal maxima and \(\theta\) is the angle of diffraction.
\[
\mathrm{n}=\frac{1}{\lambda \mathrm{N}}=\frac{1}{6.25 \times 10^{-7} \times 2 \times 10^{5}}=8
\]
\(\therefore\) Number of maxima \(=2 \mathrm{n}+1=2 \times 8+1=17\)
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