Question 180: Waves Optics

Question

If $${I_0}$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

Accepted Answer

$$I = {I_0}{\left( {{{\sin 	heta } \over 	heta }} ight)^2}$$
and $$	heta  = {\pi  \over \lambda }\left( {{{ay} \over D}} ight)$$
For principal maximum y = 0
$$ 	herefore $$ $$	heta $$ = 0
When $	heta = 0$, the intensity formula becomes :
$I = I_0\left(\frac{\sin 	heta}{	heta}ight)^2 = I_0\left(\frac{\sin 0}{0}ight)^2$
Here, we have an indeterminate form $\frac{0}{0}$. However, by taking the limit of the expression as $	heta$ approaches 0, we find that :
$\lim\limits_{	heta 	o 0} \left(\frac{\sin 	heta}{	heta}ight) = 1$
Therefore, the intensity at the principal maximum remains the same :
$I = I_0\left(\frac{\sin 	heta}{	heta}ight)^2 = I_0(1)^2 = I_0$
Hence intensity will remain same.

Answer

$$4{I_0}$$

Answer

$$2{I_0}$$

Answer

$${{{I_0}} \over 2}$$

Answer

$${I_0}$$

Waves Optics

If ${I_0}$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

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