A) 400 nm, 500 nm
B)
625 nm, 500 nm C)
380 nm, 500 nm
D)
380 nm, 525 nm
Correct Answer:
B Solution :
In question \[\theta =\frac{1}{40}\] which is very small \[\therefore \text{ }sin\text{ }\theta =\theta =\frac{1}{40}\] \[d\times \theta =n\lambda ,\] \[n\,\,=\,\,\frac{d\theta }{\lambda }\,\,=\,\,\frac{0.1\,mm}{40\,\lambda }\] \[n=\frac{2500}{\lambda }nm\,\] When \[\lambda =380\] \[{{n}_{1}}\,=\,\frac{2500}{350}\,\,=\,\,6.578\] \[for\,\,\lambda =740\,nm\] \[{{n}_{2}}\,=\,\frac{2500}{740}\,=\,3.378\] \[\therefore \,\,\,\,n=4,\,\,5,\,\,6\] \[for\text{ }n=4,\text{ }\lambda =625\text{ }nm\] \[for\text{ }n=5,\text{ }\lambda =500\text{ }nm\]
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