Question 277: Waves Optics

Question

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength $6000 \mathop A\limits^o$. If the slit is illuminated by light of another wavelength, the angular separation decreases by $20 \%$. The wavelength of light used is

Accepted Answer

The angular width of the central maximum in a Fraunhofer diffraction pattern is given by:
$  	heta = \frac{2\lambda}{a}  $
This implies that:
$ 	heta \propto \lambda  $
Therefore, if the angle changes when a different wavelength is used, we get:
$ \frac{	heta_2}{	heta_1} = \frac{\lambda_2}{\lambda_1} $
Given that the angular separation decreases by 20% when a new wavelength is used, we have:
$ 	heta_2 = 	heta_1 - \frac{20}{100} 	heta_1 = 0.8 	heta_1 $
Thus:
$ \lambda_2 = 0.8 \lambda_1 = 0.8 	imes 6000 = 4800 \mathop A\limits^o $
Therefore, the wavelength of the light used is $4800 \mathop A\limits^o$.

Answer

$6400 \mathop A\limits^o$

Answer

$5600 \mathop A\limits^o$

Answer

$4800 \mathop A\limits^o$

Answer

$4400 \mathop A\limits^o$

Waves Optics

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