91影视

Previously signal wavelength is $50\mathrm{cm}$and for digital television, the signal wavelength is $10\text{mm}$.

The slit width,$\text{a}=5\text{m}$.

The expression for the minima in the diffraction pattern is given as follows.

$\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{胃}\mathbf{=}\mathit{m}\mathit{位}$ $\mathbf{\left(}\mathbf{1}\mathbf{\right)}$

Here, $\mathbf{a}$is the slit width, $\mathit{位}$is the wavelength,$\mathbf{m}$is the number of fringes in the envelope, andlocalid="1663139465827" $\mathit{胃}$is the angle of diffraction

From equation (1), it can be concluded that the angle of the diffraction is directly proportional to the wavelength.

Since the wavelength decreases from $50\text{cm}$to $10\text{mm}$. Therefore, the angle of diffraction is also decreases. Thus, decreasing the diffraction of the signal into a shadow region is the obstacle.

Hence decreasing the diffraction of the signal into a shadow region is the obstacle.

Recall the equation (1),

$$\begin{gathered} a\sin 胃=m位 \\ \sin 胃=\frac{m位}{a} \\ 胃={\sin }^{-1}\left(\frac{m位}{a}\right) \end{gathered}$$ (2)

The angular spread is double of the angle of diffraction.

Multiply the equation (2) by 2.

$2胃={\sin }^{-1}\left(\frac{m位}{a}\right)$

Substitute $1$for $m$, $50\text{cm}$for $位$, and $5\text{m}$for$a$into the above equation.

localid="1664271350398" $$\begin{gathered} 2胃=2{\sin }^{-1}\left(\frac{1脳50脳{10}^{-2}\text{m}}{5\text{m}}\right) \\ 2胃=2{\sin }^{-1}\left(0.1\right) \\ 2胃=2脳5.73掳 \\ 2胃=11.4掳 \end{gathered}$$

Hence the angular spread is$11.4掳$.

Recall the equation (1),

$$\begin{gathered} a\sin 胃=m位 \\ \sin 胃=\frac{m位}{a} \\ 胃={\sin }^{-1}\left(\frac{m位}{a}\right) \end{gathered}$$ (3)

The angular spread is double of the angle of diffraction.

Multiply the equation (3) by 2.

$2胃={\sin }^{-1}\left(\frac{m位}{a}\right)$

Substitute $1$for $m$, $10\mathrm{mm}$for $位$, and $5\mathrm{m}$for $a$into the above equation.

localid="1664271363740" $$\begin{gathered} 2胃=2{\sin }^{-1}\left(\frac{1脳10脳{10}^{-3}m}{5m}\right) \\ 2胃=2{\sin }^{-1}\left(2脳{10}^{-3}\right) \\ 2胃=2脳0.114掳 \\ 2胃=0.23掳 \end{gathered}$$

Hence the angular spread is $0.23掳$.