Optics Question 168
Question: Angular width of central maxima in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength $ 6000{AA} $ . When the slit is illuminated by light of another wavelength, the angular width decreases by 30%. The wavelength of this light will be
Options:
A) $ 6000{AA} $
B) $ 4200{AA} $
C) $ 3000{AA} $
D) $ 1800{AA} $
Show Answer
Answer:
Correct Answer: B
Solution:
Angular width $ \beta $
$ =\frac{2\lambda }{d} $
$ \Rightarrow \frac{{\beta _{1}}}{{\beta _{2}}}=\frac{{\lambda _{1}}}{{\lambda _{2}}}\Rightarrow \frac{\beta }{\frac{70}{100}\beta }=\frac{6000}{{\lambda _{2}}}\Rightarrow {\lambda _{2}}=4200{AA} $
