有條物理唔識做(wave)

2007-10-14 3:47 am

A beam of microwaves of wavelength 3.1cm is directed normally through a double slit in
a metal screen and interference effects are detected in a plane parallel to the slits and at a distance of 40cm from them. It is found that the distance between the centres of the first maxima on either side of the central maximum in the interference pattern is 70cm. Calculate a value for the slit separation.
Ans is 4.7cm

回答 (1)

天同

2007-10-14 5:17 am

✔ 最佳答案

Use the formula : a.sin(p) = m.w
where a is the slit separation,
p is the angle substended by the m-th order maximum with the central maximum,
and w is the wavelength of wave used.
Now, m = 1
thus, a = w/sin(p)
since the first order maximum is at a distance of 70/2 cm = 35 cm from the central maximum
sin(p) = 35/sqrt(35^2+40^2) = 0.6585
hence, a = 3.1/0.6585 cm = 4.71 cm
The formula that you used is only valid for small angle of p. In the derivation of that formula, the assumption that sin(p)=tan(p) has been used.
But in this problem, the angle p is about 41.18 degrees. At such angle, the sine and tangent of the angle cannot be assumed to be equal.

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