Question 22: Wave Optics

Question

An EM wave of frequency $5 	imes 10^9 \mathrm{~Hz}$ falls normally on a rectangular slit of width 3 cm . What is the total angular width of the central maxima?

Accepted Answer

First, find the wavelength
$$\lambda=\frac{c}{f}=\frac{3	imes10^8m\,m/s}{5	imes10^9m\,Hz}=0.06m\,m=6\,cm.$$
For a single slit of width $a=3$ cm, the first minima satisfy
$$a\sin	heta=\lambda\quad\Longrightarrow\quad\sin	heta=\frac{\lambda}{a}=\frac{6}{3}=2,$$
which has no real solution (i.e.\ no true minima within $\pm90^\circ$).  In practice one then uses the small-angle approximation
$$\sin	heta\approx	heta\,,\quad	heta\approx\frac{\lambda}{a}=2m\ rad.$$
The total angular width of the central maximum (from $-	heta$ to $+	heta$) is
$$2	heta\approx2	imes2=4m\ rad.$$
Answer: Option C (4 rad).

Answer

8 rad

Answer

2 rad

Answer

4 rad

Answer

0.25 rad

Wave Optics

An EM wave of frequency 5 \times 10^9 \mathrm{~Hz} falls normally on a rectangular slit of width 3 cm . What is the total angular width of the central maxima?

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