91影视

Near point of the person is, $P_n=25.0鈥�\mathrm{cm}$.

Focal length of the lens is, $f=10鈥�\mathrm{cm}$.

Angular magnification is the ratio of the angular height with magnifier to the angular height without magnifier. For virtual image,$\mathit{i}\mathbf{<}\mathbf{0}$Using this, we can find the required quantities.

Formula:

Angular height$\mathit{胃}\mathbf{=}\frac{\mathbf{h}}{{\mathbf{P}}_{\mathbf{n}}}$

Angular height with magnifier${\mathit{胃}}^{\mathbf{\text{'}}}\mathbf{=}\frac{\mathbf{h}}{{\mathbf{P}}_{\mathbf{n}}}$

Angular magnification${\mathit{m}}_{\mathbf{胃}}\mathbf{=}\frac{\mathbf{胃}\mathbf{\text{'}}}{\mathbf{胃}}$

Lens equation $\frac{\mathbf{1}}{\mathbf{P}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{i}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{f}}$

We have,

The angular height without magnifier is, $胃=\frac{h}{P_n}$

And angular height with magnifier is, ${胃}^{\text{'}}=\frac{h}{P}$

Now, we can find the position of the virtual image formed by the lens.

Since

$\frac{1}{P}=\frac{1}{f}-\frac{1}{i}$

As the image is virtual, $i=-\left|i\right|=P_n$

Therefore,

$\frac{1}{P}=\frac{1}{f}+\frac{1}{\left|i\right|}$

$=\frac{1}{f}+\frac{1}{P_n}$

Then the angular magnification is

$m_{胃}=\frac{胃\text{'}}{胃}$

$\begin{array}{c}=\left(\frac{h/P}{h/P_n}\right)\\ =\left(\frac{1/P}{1/P_n}\right)\end{array}$

$\begin{array}{c}{m}_{胃}=\frac{\left(\frac{1}{f}+\frac{1}{P_n}\right)}{\frac{1}{P_n}}\\ =\frac{P_n}{f}+1\\ =\frac{25鈥�\mathrm{cm}}{f}+1\end{array}$

For focal length $f$, the angular magnification of the magnifier is,$m_{胃}=1+\frac{25鈥�\mathrm{cm}}{f}$

If object is moved so that its image appears at infinity,

then $i=-\left|i\right|鈫�-鈭�$.

$\begin{array}{c}\frac{1}{P}=\frac{1}{f}+\frac{1}{\left|i\right|}\\ =\frac{1}{f}+\frac{1}{鈭�}\\ =\frac{1}{f}\end{array}$

Then the angular magnification is

$m_{胃}^{\text{'}}=\frac{胃\text{'}}{胃}$

$=\left(\frac{h/p}{h/p_n}\right)$

$=\left(\frac{1/p}{1/p_n}\right)$

$\begin{array}{c}{m}_{胃}^{\text{'}}=\frac{P_n}{f}\\ =\frac{25鈥�\mathrm{cm}}{f}\end{array}$

For focal length$f,$ the angular magnification if the object is moved so that its image appears at infinity is,

$m_{胃}^{\text{'}}=\frac{25鈥�\mathrm{cm}}{f}$

For$f=10鈥�\mathrm{cm}$, the angular magnification of magnifier is

$\begin{array}{c}{m}_{胃}=\frac{P_n}{f}+1\\ =\frac{25鈥�\mathrm{cm}}{10鈥�\mathrm{cm}}+1\\ =3.5\end{array}$

For $f=10鈥�\mathrm{cm}$, the angular magnification of the magnifier is $\begin{array}{c}{m}_{胃}=3.5\end{array}$

For $f=10鈥�\mathrm{cm}$, the angular magnification if the object is moved so that its image appears at infinity is

$\begin{array}{c}{m}_{胃}^{\text{'}}=\frac{P_n}{f}\\ =\frac{25鈥�\mathrm{cm}}{10鈥�\mathrm{cm}}\\ =2.5\end{array}$

For $f=10鈥�\mathrm{cm}$, the angular magnification if the object is moved so that its image appears at infinity is $m_{胃}^{\text{'}}=2.5$