Question 11: Units , Dimensions and Error Analysis

Question

If E is the amplitude of the electric field of the waves starting from the slits in a double slit experiment and $	heta$ is the phase difference between the waves reaching a point on the screen, the ratio of the amplitude of the resultant electric field at that point on the screen to the amplitude at one of the slits is

Accepted Answer

When you add two equalÃ¢ÂÂamplitude waves with a phase difference ÃÂ¸ as phasors, you get
$$E_{m res} \;=\; E\bigl(e^{i0}+e^{i	heta}\bigr) \;=\;2E\cos\!\Bigl(\frac{	heta}{2}\Bigr)\,e^{\,i	heta/2}\,. $$
The magnitude of the resultant amplitude is
$$\bigl|E_{m res}\bigr|=2E\cos\!\Bigl(\frac{	heta}{2}\Bigr),$$
so the ratio to the singleÃ¢ÂÂslit amplitude E is
$$\frac{|E_{m res}|}{E}=2\cos\!\Bigl(\frac{	heta}{2}\Bigr).$$
That corresponds to Option D.

Answer

$\cos (	heta)$

Answer

$2 \cos (	heta)$

Answer

$\cos \left(\frac{	heta}{2}ight)$

Answer

$2 \cos \left(\frac{	heta}{2}ight)$

Units , Dimensions and Error Analysis

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